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<h2> <a href="science.html"> ⇦ Back to Science chapter list</a></h2>
<section class="sv-section">
<h1>Doppler effect</h1>
<section class="sv-section">
<h2>1. Introduction</h2>
</section> <section class="sv-section">
<h2>2. The Doppler effect with sound</h2>
<hr><section class="sv-section sv-question sv-table"><br><div class="id2029-7399">ID is: 2029 Seed is: 7399<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/455789eb-be43-5315-ba8c-57c1a4853176" method="POST">
<span class="worked_example"><h3 class="sv-heading">The Doppler effect with sound</h3>
</span><div class="problem">
<p>
Match each item in Column A with the correct option from the table below. Indicate your choice by choosing the corresponding symbols (A to H) in Column B.
</p>
<p align="center">
</p><table border="1">
<tbody><tr> <th align="center">Symbol</th> <th align="center">Options</th></tr>
<tr> <td align="center"> A </td> <td width="300"> The pitch of the observed sound goes down due to an apparent decrease in frequency. </td> </tr>
<tr> <td align="center"> B </td> <td width="300"> Sound waves with a frequency greater than 20 000 Hz. </td> </tr>
<tr> <td align="center"> C </td> <td width="300"> The object or person that is hearing or measuring the sound. </td> </tr>
<tr> <td align="center"> D </td> <td width="300"> The object or person that is producing the sound. </td> </tr>
<tr> <td align="center"> E </td> <td width="300"> An aspect of sound waves which changes due to the Doppler effect. </td> </tr>
<tr> <td align="center"> F </td> <td width="300"> The use of ultrasound equipment in medicine. </td> </tr>
<tr> <td align="center"> G </td> <td width="300"> The pitch of the observed sound goes up due to an apparent increase in frequency. </td> </tr>
<tr> <td align="center"> H </td> <td width="300"> When a source of waves and/or an observer move relative to each other, resulting in the observer measuring a different frequency of the waves than the frequency that the source is emitting. </td> </tr>
</tbody></table>
<p></p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p align="center">
</p><table border="1">
<tbody><tr> <th align="center">Column A</th> <th align="center">Column B</th></tr>
<tr> <td align="left" width="150"> This happens when a source approaches a stationary observer. </td> <td> <select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">A</option><option value="1">B</option><option value="2">C</option><option value="3">D</option><option value="4">E</option><option value="5">F</option><option value="6" selected="">G</option><option value="7">H</option></select> </td> </tr>
<tr> <td align="left" width="150"> source </td> <td> <select name="question1b" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">A</option><option value="1">B</option><option value="2">C</option><option value="3" selected="">D</option><option value="4">E</option><option value="5">F</option><option value="6">G</option><option value="7">H</option></select> </td> </tr>
<tr> <td align="left" width="150"> pitch </td> <td> <select name="question1c" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">A</option><option value="1">B</option><option value="2">C</option><option value="3">D</option><option value="4" selected="">E</option><option value="5">F</option><option value="6">G</option><option value="7">H</option></select> </td> </tr>
</tbody></table>
<p></p>
</div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:42:00.359014"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><section class="sv-section sv-question sv-table"><br><div class="id2029-7138">ID is: 2029 Seed is: 7138<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/455789eb-be43-5315-ba8c-57c1a4853176" method="POST">
<span class="worked_example"><h3 class="sv-heading">The Doppler effect with sound</h3>
</span><div class="problem">
<p>
Match each item in Column A with the correct option from the table below. Indicate your choice by choosing the corresponding symbols (A to H) in Column B.
</p>
<p align="center">
</p><table border="1">
<tbody><tr> <th align="center">Symbol</th> <th align="center">Options</th></tr>
<tr> <td align="center"> A </td> <td width="300"> The object or person that is hearing or measuring the sound. </td> </tr>
<tr> <td align="center"> B </td> <td width="300"> Sound waves with a frequency greater than 20 000 Hz. </td> </tr>
<tr> <td align="center"> C </td> <td width="300"> The pitch of the observed sound goes up due to an apparent increase in frequency. </td> </tr>
<tr> <td align="center"> D </td> <td width="300"> The use of ultrasound equipment in medicine. </td> </tr>
<tr> <td align="center"> E </td> <td width="300"> An aspect of sound waves which changes due to the Doppler effect. </td> </tr>
<tr> <td align="center"> F </td> <td width="300"> When a source of waves and/or an observer move relative to each other, resulting in the observer measuring a different frequency of the waves than the frequency that the source is emitting. </td> </tr>
<tr> <td align="center"> G </td> <td width="300"> The pitch of the observed sound goes down due to an apparent decrease in frequency. </td> </tr>
<tr> <td align="center"> H </td> <td width="300"> The object or person that is producing the sound. </td> </tr>
</tbody></table>
<p></p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p align="center">
</p><table border="1">
<tbody><tr> <th align="center">Column A</th> <th align="center">Column B</th></tr>
<tr> <td align="left" width="150"> This happens when a source recedes from a stationary observer. </td> <td> <select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">A</option><option value="1">B</option><option value="2">C</option><option value="3">D</option><option value="4">E</option><option value="5">F</option><option value="6" selected="">G</option><option value="7">H</option></select> </td> </tr>
<tr> <td align="left" width="150"> ultrasound </td> <td> <select name="question1b" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">A</option><option value="1" selected="">B</option><option value="2">C</option><option value="3">D</option><option value="4">E</option><option value="5">F</option><option value="6">G</option><option value="7">H</option></select> </td> </tr>
<tr> <td align="left" width="150"> pitch </td> <td> <select name="question1c" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">A</option><option value="1">B</option><option value="2">C</option><option value="3">D</option><option value="4" selected="">E</option><option value="5">F</option><option value="6">G</option><option value="7">H</option></select> </td> </tr>
</tbody></table>
<p></p>
</div></div></div>
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<span class="worked_example"><h3 class="sv-heading">Multiple choice: Doppler effect</h3>
</span><div class="problem">
<p>
<span class="colored" style="color:gray"><em>Adapted from DBE Feb-Mar 2017 Grade 12, P1, Q1.6</em></span> <br>
<a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">Physical constants</a> · <a url="/info/physics-formulas" href="https://www.emas.com/info/physics-formulas">Physics formulas</a>
</p>
<p>
A observer hears a sound coming from a stationary sound source. The sound that the observer hears has a higher frequency when compared to that produced by the source.
</p>
<p>
What can you conclude about the observer from this observation?
</p>
<table border="1"> <tbody><tr> <td style="background:lightgray"><strong>A</strong></td> <td>The observer is at rest.</td></tr><tr> <td style="background:lightgray"><strong>B</strong></td> <td>The observer is moving towards the source.</td></tr><tr> <td style="background:lightgray"><strong>C</strong></td> <td>The observer is moving away from the source.</td></tr><tr> <td style="background:lightgray"><strong>D</strong></td> <td>There is an obstacle between the source and the observer.</td></tr></tbody></table>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">A</option><option value="1" selected="">B</option><option value="2">C</option><option value="3">D</option></select>
</div></div></div>
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</div></section><section class="sv-section sv-question sv-table"><br><div class="id3840-4122">ID is: 3840 Seed is: 4122<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/455789eb-be43-5315-ba8c-57c1a4853176" method="POST">
<span class="worked_example"><h3 class="sv-heading">Multiple choice: Doppler effect</h3>
</span><div class="problem">
<p>
<span class="colored" style="color:gray"><em>Adapted from DBE Feb-Mar 2017 Grade 12, P1, Q1.6</em></span> <br>
<a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">Physical constants</a> · <a url="/info/physics-formulas" href="https://www.emas.com/info/physics-formulas">Physics formulas</a>
</p>
<p>
A observer hears a sound coming from a stationary sound source. The sound that the observer hears has a higher pitch when compared to that produced by the source.
</p>
<p>
What can you conclude about the observer from this observation?
</p>
<table border="1"> <tbody><tr> <td style="background:lightgray"><strong>A</strong></td> <td>The observer is at rest.</td></tr><tr> <td style="background:lightgray"><strong>B</strong></td> <td>The observer is moving towards the source.</td></tr><tr> <td style="background:lightgray"><strong>C</strong></td> <td>The observer is moving away from the source.</td></tr><tr> <td style="background:lightgray"><strong>D</strong></td> <td>The air between the source and the observer is hot and damp.</td></tr></tbody></table>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">A</option><option value="1" selected="">B</option><option value="2">C</option><option value="3">D</option></select>
</div></div></div>
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</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id2025-764">ID is: 2025 Seed is: 764<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/455789eb-be43-5315-ba8c-57c1a4853176" method="POST">
<span class="worked_example"><h3 class="sv-heading">The Doppler effect: sound waves</h3>
</span><div class="problem">
<p>
A person is riding in a taxi which is travelling at a speed of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-1-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>26,49</mtext><mtext>&#xA0;</mtext><msup><mtext>km&#xB7;h</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1" style="width: 6.385em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.214em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1005.21em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-2"><span class="mtext" id="MathJax-Span-3" style="font-family: STIXGeneral;">26,49</span><span class="mtext" id="MathJax-Span-4" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-5"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px;"><span style="position: absolute; clip: rect(3.106em, 1001.99em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-6" style="font-family: STIXGeneral;">km·h</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.388em; left: 2.052em;"><span class="mtext" id="MathJax-Span-7" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>26,49</mtext><mtext> </mtext><msup><mtext>km·h</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-1">\text{26,49} ~\text{km·h}^\text{-1}</script></span>.</span> Traveling in the opposite direction to the taxi is a mechanical street sweeper, receding (moving away) at a speed of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-2-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>45,49</mtext><mtext>&#xA0;</mtext><msup><mtext>km&#xB7;h</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-8" style="width: 6.385em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.214em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1005.21em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-9"><span class="mtext" id="MathJax-Span-10" style="font-family: STIXGeneral;">45,49</span><span class="mtext" id="MathJax-Span-11" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-12"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px;"><span style="position: absolute; clip: rect(3.106em, 1001.99em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-13" style="font-family: STIXGeneral;">km·h</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.388em; left: 2.052em;"><span class="mtext" id="MathJax-Span-14" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>45,49</mtext><mtext> </mtext><msup><mtext>km·h</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-2">\text{45,49} ~\text{km·h}^\text{-1}</script></span>.</span> The warning signal of the mechanical street sweeper produces a sound wave with a frequency of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-3-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>728,54</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-15" style="width: 5.097em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.16em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.16em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-16"><span class="mtext" id="MathJax-Span-17" style="font-family: STIXGeneral;">728,54</span><span class="mtext" id="MathJax-Span-18" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-19" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>728,54</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-3">\text{728,54} ~\text{Hz}</script></span>.</span> The person riding in the taxi hears the sound wave produced by the warning signal of the mechanical street sweeper at an apparent frequency of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-4-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>686,64</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-20" style="width: 5.097em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.16em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.16em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-21"><span class="mtext" id="MathJax-Span-22" style="font-family: STIXGeneral;">686,64</span><span class="mtext" id="MathJax-Span-23" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-24" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>686,64</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-4">\text{686,64} ~\text{Hz}</script></span>.</span>
</p>
<p>
Use the above information to determine the following:
</p>
<p>
What is the speed of sound at the prevailing conditions?
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
<ul>
<li>Round your answer to <strong>two decimal places</strong>.</li>
<li>Use the values for any physical constants you might need, as listed <a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">here</a>.</li>
</ul>
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
The speed of sound at the prevailing conditions is <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="335,02" size="10"> <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-5-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><msup><mtext>m&#xB7;s</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-25" style="width: 2.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.345em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1002.35em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-26"><span class="mtext" id="MathJax-Span-27" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-28"><span style="display: inline-block; position: relative; width: 2.111em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1001.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-29" style="font-family: STIXGeneral;">m·s</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 1.408em;"><span class="mtext" id="MathJax-Span-30" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><msup><mtext>m·s</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-5">~\text{m·s}^\text{-1}</script></span>.</span>
<div class="response-type">numeric</div></div></div></div>
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</div></section><section class="sv-section sv-question sv-table"><br><div class="id2025-660">ID is: 2025 Seed is: 660<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/455789eb-be43-5315-ba8c-57c1a4853176" method="POST">
<span class="worked_example"><h3 class="sv-heading">The Doppler effect: sound waves</h3>
</span><div class="problem">
<p>
A person is riding in a pickup truck which is travelling at a speed of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-6-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>21,51</mtext><mtext>&#xA0;</mtext><msup><mtext>km&#xB7;h</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-31" style="width: 6.385em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.214em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1005.21em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-32"><span class="mtext" id="MathJax-Span-33" style="font-family: STIXGeneral;">21,51</span><span class="mtext" id="MathJax-Span-34" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-35"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px;"><span style="position: absolute; clip: rect(3.106em, 1001.99em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-36" style="font-family: STIXGeneral;">km·h</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.388em; left: 2.052em;"><span class="mtext" id="MathJax-Span-37" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>21,51</mtext><mtext> </mtext><msup><mtext>km·h</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-6">\text{21,51} ~\text{km·h}^\text{-1}</script></span>.</span> Traveling in the opposite direction to the pickup truck is an ambulance, receding (moving away) at a speed of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-7-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>83,26</mtext><mtext>&#xA0;</mtext><msup><mtext>km&#xB7;h</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-38" style="width: 6.385em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.214em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1005.21em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-39"><span class="mtext" id="MathJax-Span-40" style="font-family: STIXGeneral;">83,26</span><span class="mtext" id="MathJax-Span-41" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-42"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px;"><span style="position: absolute; clip: rect(3.106em, 1001.99em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-43" style="font-family: STIXGeneral;">km·h</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.388em; left: 2.052em;"><span class="mtext" id="MathJax-Span-44" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>83,26</mtext><mtext> </mtext><msup><mtext>km·h</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-7">\text{83,26} ~\text{km·h}^\text{-1}</script></span>.</span> The siren of the ambulance produces a sound wave with a frequency of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-8-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>695,02</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-45" style="width: 5.097em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.16em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.16em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-46"><span class="mtext" id="MathJax-Span-47" style="font-family: STIXGeneral;">695,02</span><span class="mtext" id="MathJax-Span-48" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-49" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>695,02</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-8">\text{695,02} ~\text{Hz}</script></span>.</span> The person riding in the pickup truck hears the sound wave produced by the siren of the ambulance at an apparent frequency of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-9-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>639,01</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-50" style="width: 5.097em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.16em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.16em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-51"><span class="mtext" id="MathJax-Span-52" style="font-family: STIXGeneral;">639,01</span><span class="mtext" id="MathJax-Span-53" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-54" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>639,01</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-9">\text{639,01} ~\text{Hz}</script></span>.</span>
</p>
<p>
Use the above information to determine the following:
</p>
<p>
What is the speed of sound at the prevailing conditions?
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
<ul>
<li>Round your answer to <strong>two decimal places</strong>.</li>
<li>Use the values for any physical constants you might need, as listed <a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">here</a>.</li>
</ul>
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
The speed of sound at the prevailing conditions is <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="338" size="10"> <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-10-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><msup><mtext>m&#xB7;s</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-55" style="width: 2.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.345em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1002.35em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-56"><span class="mtext" id="MathJax-Span-57" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-58"><span style="display: inline-block; position: relative; width: 2.111em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1001.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-59" style="font-family: STIXGeneral;">m·s</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 1.408em;"><span class="mtext" id="MathJax-Span-60" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><msup><mtext>m·s</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-10">~\text{m·s}^\text{-1}</script></span>.</span>
<div class="response-type">numeric</div></div></div></div>
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</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id2014-246">ID is: 2014 Seed is: 246<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/455789eb-be43-5315-ba8c-57c1a4853176" method="POST">
<span class="worked_example"><h3 class="sv-heading">The Doppler effect: sound waves</h3>
</span><div class="problem">
<p>
The siren of a mechanical street sweeper produces a sound wave with a frequency of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-11-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><mtext>413</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-61" style="width: 3.867em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.165em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.16em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-62"><span class="mtext" id="MathJax-Span-63" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-64" style="font-family: STIXGeneral;">413</span><span class="mtext" id="MathJax-Span-65" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-66" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><mtext>413</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-11">~\text{413}~\text{Hz}</script></span>.</span> You are standing at the side of the road. The mechanical street sweeper is approaching you at a speed of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-12-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>48</mtext><mtext>&#xA0;</mtext><msup><mtext>km&#xB7;h</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-67" style="width: 4.804em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.926em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1003.93em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-68"><span class="mtext" id="MathJax-Span-69" style="font-family: STIXGeneral;">48</span><span class="mtext" id="MathJax-Span-70" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-71"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px;"><span style="position: absolute; clip: rect(3.106em, 1001.99em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-72" style="font-family: STIXGeneral;">km·h</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.388em; left: 2.052em;"><span class="mtext" id="MathJax-Span-73" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>48</mtext><mtext> </mtext><msup><mtext>km·h</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-12">\text{48} ~\text{km·h}^\text{-1}</script></span>.</span> The apparent frequency of the sound wave you hear is <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-13-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><mtext>429</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-74" style="width: 3.867em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.165em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.16em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-75"><span class="mtext" id="MathJax-Span-76" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-77" style="font-family: STIXGeneral;">429</span><span class="mtext" id="MathJax-Span-78" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-79" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><mtext>429</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-13">~\text{429}~\text{Hz}</script></span>.</span>
</p>
<p>
Use the above information to determine the following:
</p>
<p>
What is the speed of the sound wave produced by the siren of the mechanical street sweeper under these conditions, or <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-14-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><mi>v</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-80" style="width: 0.94em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.764em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.876em, 1000.76em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-81"><span class="mtext" id="MathJax-Span-82" style="font-family: STIXGeneral;"> </span><span class="mi" id="MathJax-Span-83" style="font-family: STIXGeneral; font-style: italic;">𝑣</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><mi>v</mi></math></span></span><script type="math/tex" id="MathJax-Element-14">~v</script></span>?</span>
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
<ul>
<li>Round your answer to <strong>two decimal places</strong>.</li>
<li>Use the values for any physical constants you might need, as listed <a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">here</a>.</li>
</ul>
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
The speed of the sound wave is: <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="357,5" size="10"> <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-15-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><msup><mtext>m&#xB7;s</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-84" style="width: 2.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.345em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1002.35em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-85"><span class="mtext" id="MathJax-Span-86" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-87"><span style="display: inline-block; position: relative; width: 2.111em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1001.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-88" style="font-family: STIXGeneral;">m·s</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 1.408em;"><span class="mtext" id="MathJax-Span-89" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><msup><mtext>m·s</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-15">~\text{m·s}^\text{-1}</script></span>.</span>
<div class="response-type">numeric</div></div></div></div>
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</div></section><section class="sv-section sv-question sv-table"><br><div class="id2014-5268">ID is: 2014 Seed is: 5268<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/455789eb-be43-5315-ba8c-57c1a4853176" method="POST">
<span class="worked_example"><h3 class="sv-heading">The Doppler effect: sound waves</h3>
</span><div class="problem">
<p>
The siren of a garbage truck produces a sound wave with a frequency of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-16-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><mtext>518</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-90" style="width: 3.867em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.165em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.16em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-91"><span class="mtext" id="MathJax-Span-92" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-93" style="font-family: STIXGeneral;">518</span><span class="mtext" id="MathJax-Span-94" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-95" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><mtext>518</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-16">~\text{518}~\text{Hz}</script></span>.</span> You are standing at the side of the road. The garbage truck is approaching you at a speed of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-17-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>45</mtext><mtext>&#xA0;</mtext><msup><mtext>km&#xB7;h</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-96" style="width: 4.804em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.926em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1003.93em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-97"><span class="mtext" id="MathJax-Span-98" style="font-family: STIXGeneral;">45</span><span class="mtext" id="MathJax-Span-99" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-100"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px;"><span style="position: absolute; clip: rect(3.106em, 1001.99em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-101" style="font-family: STIXGeneral;">km·h</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.388em; left: 2.052em;"><span class="mtext" id="MathJax-Span-102" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>45</mtext><mtext> </mtext><msup><mtext>km·h</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-17">\text{45} ~\text{km·h}^\text{-1}</script></span>.</span> The apparent frequency of the sound wave you hear is <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-18-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><mtext>537</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-103" style="width: 3.867em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.165em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.16em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-104"><span class="mtext" id="MathJax-Span-105" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-106" style="font-family: STIXGeneral;">537</span><span class="mtext" id="MathJax-Span-107" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-108" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><mtext>537</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-18">~\text{537}~\text{Hz}</script></span>.</span>
</p>
<p>
Use the above information to determine the following:
</p>
<p>
What is the speed of the sound wave produced by the siren of the garbage truck under these conditions, or <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-19-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><mi>v</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-109" style="width: 0.94em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.764em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.876em, 1000.76em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-110"><span class="mtext" id="MathJax-Span-111" style="font-family: STIXGeneral;"> </span><span class="mi" id="MathJax-Span-112" style="font-family: STIXGeneral; font-style: italic;">𝑣</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><mi>v</mi></math></span></span><script type="math/tex" id="MathJax-Element-19">~v</script></span>?</span>
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
<ul>
<li>Round your answer to <strong>two decimal places</strong>.</li>
<li>Use the values for any physical constants you might need, as listed <a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">here</a>.</li>
</ul>
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
The speed of the sound wave is: <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="353,29" size="10"> <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-20-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><msup><mtext>m&#xB7;s</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-113" style="width: 2.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.345em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1002.35em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-114"><span class="mtext" id="MathJax-Span-115" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-116"><span style="display: inline-block; position: relative; width: 2.111em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1001.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-117" style="font-family: STIXGeneral;">m·s</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 1.408em;"><span class="mtext" id="MathJax-Span-118" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><msup><mtext>m·s</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-20">~\text{m·s}^\text{-1}</script></span>.</span>
<div class="response-type">numeric</div></div></div></div>
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</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id2024-7788">ID is: 2024 Seed is: 7788<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/455789eb-be43-5315-ba8c-57c1a4853176" method="POST">
<span class="worked_example"><h3 class="sv-heading">The Doppler effect: sound waves</h3>
</span><div class="problem">
<p>
The reversing signal of a construction vehicle produces a sound wave with a certain frequency. You are standing at a hot dog stand. The construction vehicle is approaching you at a speed of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-21-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>33</mtext><mtext>&#xA0;</mtext><msup><mtext>km&#xB7;h</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-119" style="width: 4.804em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.926em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1003.93em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-120"><span class="mtext" id="MathJax-Span-121" style="font-family: STIXGeneral;">33</span><span class="mtext" id="MathJax-Span-122" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-123"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px;"><span style="position: absolute; clip: rect(3.106em, 1001.99em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-124" style="font-family: STIXGeneral;">km·h</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.388em; left: 2.052em;"><span class="mtext" id="MathJax-Span-125" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>33</mtext><mtext> </mtext><msup><mtext>km·h</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-21">\text{33} ~\text{km·h}^\text{-1}</script></span>.</span> The apparent frequency of the sound wave you hear is <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-22-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><mtext>440</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-126" style="width: 3.867em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.165em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.16em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-127"><span class="mtext" id="MathJax-Span-128" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-129" style="font-family: STIXGeneral;">440</span><span class="mtext" id="MathJax-Span-130" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-131" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><mtext>440</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-22">~\text{440}~\text{Hz}</script></span>.</span> Assume that the speed of sound is <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-23-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>347</mtext><mtext>&#xA0;</mtext><msup><mtext>m&#xB7;s</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-132" style="width: 4.745em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.867em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1003.87em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-133"><span class="mtext" id="MathJax-Span-134" style="font-family: STIXGeneral;">347</span><span class="mtext" id="MathJax-Span-135" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-136"><span style="display: inline-block; position: relative; width: 2.111em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1001.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-137" style="font-family: STIXGeneral;">m·s</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 1.408em;"><span class="mtext" id="MathJax-Span-138" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>347</mtext><mtext> </mtext><msup><mtext>m·s</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-23">\text{347}~\text{m·s}^\text{-1}</script></span>.</span>
</p>
<p>
Use the above information to determine the following:
</p>
<p>
What is the frequency of the sound wave produced by the approaching construction vehicle, or <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-24-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><msub><mi>f</mi><mi>S</mi></msub></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-139" style="width: 1.642em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.35em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.35em, 2.872em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-140"><span class="mtext" id="MathJax-Span-141" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-142"><span style="display: inline-block; position: relative; width: 1.115em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.65em, 4.335em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-143" style="font-family: STIXGeneral; font-style: italic;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.53em;"><span class="mi" id="MathJax-Span-144" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑆<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><msub><mi>f</mi><mi>S</mi></msub></math></span></span><script type="math/tex" id="MathJax-Element-24">~f_S</script></span>?</span>
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
<ul>
<li>Round your answer to <strong>two decimal places.</strong></li>
<li>Use the values for any physical constants you might need, as listed <a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">here</a>.</li>
</ul>
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-25-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mi>S</mi></msub><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-145" style="width: 2.579em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.111em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1002.05em, 2.872em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-146"><span class="msubsup" id="MathJax-Span-147"><span style="display: inline-block; position: relative; width: 1.115em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.65em, 4.335em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-148" style="font-family: STIXGeneral; font-style: italic;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.53em;"><span class="mi" id="MathJax-Span-149" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑆<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-150" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mi>S</mi></msub><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-25">f_S = </script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="428,38" size="10"> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-26-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-151" style="width: 1.467em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.174em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.17em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-152"><span class="mtext" id="MathJax-Span-153" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-26">\text{Hz}</script></span>
<div class="response-type">numeric</div></div></div></div>
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</div></section><section class="sv-section sv-question sv-table"><br><div class="id2024-8684">ID is: 2024 Seed is: 8684<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/455789eb-be43-5315-ba8c-57c1a4853176" method="POST">
<span class="worked_example"><h3 class="sv-heading">The Doppler effect: sound waves</h3>
</span><div class="problem">
<p>
The siren of an ambulance produces a sound wave with a certain frequency. You are standing at a bus stop shelter. The ambulance is approaching you at a speed of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-27-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>94</mtext><mtext>&#xA0;</mtext><msup><mtext>km&#xB7;h</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-154" style="width: 4.804em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.926em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1003.93em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-155"><span class="mtext" id="MathJax-Span-156" style="font-family: STIXGeneral;">94</span><span class="mtext" id="MathJax-Span-157" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-158"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px;"><span style="position: absolute; clip: rect(3.106em, 1001.99em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-159" style="font-family: STIXGeneral;">km·h</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.388em; left: 2.052em;"><span class="mtext" id="MathJax-Span-160" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.289em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>94</mtext><mtext> </mtext><msup><mtext>km·h</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-27">\text{94} ~\text{km·h}^\text{-1}</script></span>.</span> The apparent frequency of the sound wave you hear is <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-28-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><mtext>776</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-161" style="width: 3.867em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.165em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.16em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-162"><span class="mtext" id="MathJax-Span-163" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-164" style="font-family: STIXGeneral;">776</span><span class="mtext" id="MathJax-Span-165" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-166" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><mtext>776</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-28">~\text{776}~\text{Hz}</script></span>.</span> Assume that the speed of sound is <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-29-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>335</mtext><mtext>&#xA0;</mtext><msup><mtext>m&#xB7;s</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-167" style="width: 4.745em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.867em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1003.87em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-168"><span class="mtext" id="MathJax-Span-169" style="font-family: STIXGeneral;">335</span><span class="mtext" id="MathJax-Span-170" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-171"><span style="display: inline-block; position: relative; width: 2.111em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1001.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-172" style="font-family: STIXGeneral;">m·s</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 1.408em;"><span class="mtext" id="MathJax-Span-173" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>335</mtext><mtext> </mtext><msup><mtext>m·s</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-29">\text{335}~\text{m·s}^\text{-1}</script></span>.</span>
</p>
<p>
Use the above information to determine the following:
</p>
<p>
What is the frequency of the sound wave produced by the approaching ambulance, or <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-30-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><msub><mi>f</mi><mi>S</mi></msub></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-174" style="width: 1.642em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.35em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.35em, 2.872em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-175"><span class="mtext" id="MathJax-Span-176" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-177"><span style="display: inline-block; position: relative; width: 1.115em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.65em, 4.335em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-178" style="font-family: STIXGeneral; font-style: italic;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.53em;"><span class="mi" id="MathJax-Span-179" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑆<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><msub><mi>f</mi><mi>S</mi></msub></math></span></span><script type="math/tex" id="MathJax-Element-30">~f_S</script></span>?</span>
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
<ul>
<li>Round your answer to <strong>two decimal places.</strong></li>
<li>Use the values for any physical constants you might need, as listed <a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">here</a>.</li>
</ul>
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-31-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mi>S</mi></msub><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-180" style="width: 2.579em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.111em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1002.05em, 2.872em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-181"><span class="msubsup" id="MathJax-Span-182"><span style="display: inline-block; position: relative; width: 1.115em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.65em, 4.335em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-183" style="font-family: STIXGeneral; font-style: italic;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.53em;"><span class="mi" id="MathJax-Span-184" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑆<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-185" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mi>S</mi></msub><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-31">f_S = </script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="715,52" size="10"> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-32-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-186" style="width: 1.467em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.174em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.17em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-187"><span class="mtext" id="MathJax-Span-188" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-32">\text{Hz}</script></span>
<div class="response-type">numeric</div></div></div></div>
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</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id2018-2101">ID is: 2018 Seed is: 2101<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/455789eb-be43-5315-ba8c-57c1a4853176" method="POST">
<span class="worked_example"><h3 class="sv-heading">The Doppler effect: sound waves</h3>
</span><div class="problem">
<p>
A person is riding in a minibus which is travelling at a speed of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-33-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>32,37</mtext><mtext>&#xA0;</mtext><msup><mtext>km&#xB7;h</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-189" style="width: 6.385em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.214em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1005.21em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-190"><span class="mtext" id="MathJax-Span-191" style="font-family: STIXGeneral;">32,37</span><span class="mtext" id="MathJax-Span-192" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-193"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px;"><span style="position: absolute; clip: rect(3.106em, 1001.99em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-194" style="font-family: STIXGeneral;">km·h</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.388em; left: 2.052em;"><span class="mtext" id="MathJax-Span-195" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>32,37</mtext><mtext> </mtext><msup><mtext>km·h</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-33">\text{32,37} ~\text{km·h}^\text{-1}</script></span>.</span> Travelling in the opposite direction to the minibus is a garbage truck, approaching at a speed of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-34-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>22,05</mtext><mtext>&#xA0;</mtext><msup><mtext>km&#xB7;h</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-196" style="width: 6.385em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.214em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1005.21em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-197"><span class="mtext" id="MathJax-Span-198" style="font-family: STIXGeneral;">22,05</span><span class="mtext" id="MathJax-Span-199" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-200"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px;"><span style="position: absolute; clip: rect(3.106em, 1001.99em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-201" style="font-family: STIXGeneral;">km·h</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.388em; left: 2.052em;"><span class="mtext" id="MathJax-Span-202" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>22,05</mtext><mtext> </mtext><msup><mtext>km·h</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-34">\text{22,05} ~\text{km·h}^\text{-1}</script></span>.</span> The warning signal of the garbage truck produces a sound wave with a frequency of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-35-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>559,41</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-203" style="width: 5.097em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.16em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.16em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-204"><span class="mtext" id="MathJax-Span-205" style="font-family: STIXGeneral;">559,41</span><span class="mtext" id="MathJax-Span-206" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-207" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>559,41</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-35">\text{559,41} ~\text{Hz}</script></span>.</span> The person riding in the minibus hears the sound wave produced by the warning signal of the garbage truck at an apparent frequency of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-36-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>584,81</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-208" style="width: 5.097em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.16em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.16em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-209"><span class="mtext" id="MathJax-Span-210" style="font-family: STIXGeneral;">584,81</span><span class="mtext" id="MathJax-Span-211" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-212" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>584,81</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-36">\text{584,81} ~\text{Hz}</script></span>.</span>
</p>
<p>
Use the above information to determine the following:
</p>
<p>
What is the speed of sound at the prevailing conditions?
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
<ul>
<li>Round your answer to <strong>two decimal places</strong>.</li>
<li>Use the values for any physical constants you might need, as listed <a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">here</a>.</li>
</ul>
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
The speed of sound at the prevailing conditions is <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="339,05" size="10"> <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-37-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><msup><mtext>m&#xB7;s</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-213" style="width: 2.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.345em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1002.35em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-214"><span class="mtext" id="MathJax-Span-215" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-216"><span style="display: inline-block; position: relative; width: 2.111em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1001.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-217" style="font-family: STIXGeneral;">m·s</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 1.408em;"><span class="mtext" id="MathJax-Span-218" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><msup><mtext>m·s</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-37">~\text{m·s}^\text{-1}</script></span>.</span>
<div class="response-type">numeric</div></div></div></div>
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</div></section><section class="sv-section sv-question sv-table"><br><div class="id2018-1105">ID is: 2018 Seed is: 1105<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/455789eb-be43-5315-ba8c-57c1a4853176" method="POST">
<span class="worked_example"><h3 class="sv-heading">The Doppler effect: sound waves</h3>
</span><div class="problem">
<p>
A person is riding in a car which is travelling at a speed of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-38-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>55,19</mtext><mtext>&#xA0;</mtext><msup><mtext>km&#xB7;h</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-219" style="width: 6.385em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.214em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1005.21em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-220"><span class="mtext" id="MathJax-Span-221" style="font-family: STIXGeneral;">55,19</span><span class="mtext" id="MathJax-Span-222" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-223"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px;"><span style="position: absolute; clip: rect(3.106em, 1001.99em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-224" style="font-family: STIXGeneral;">km·h</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.388em; left: 2.052em;"><span class="mtext" id="MathJax-Span-225" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>55,19</mtext><mtext> </mtext><msup><mtext>km·h</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-38">\text{55,19} ~\text{km·h}^\text{-1}</script></span>.</span> Travelling in the opposite direction to the car is a garbage truck, approaching at a speed of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-39-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>26,14</mtext><mtext>&#xA0;</mtext><msup><mtext>km&#xB7;h</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-226" style="width: 6.385em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.214em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1005.21em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-227"><span class="mtext" id="MathJax-Span-228" style="font-family: STIXGeneral;">26,14</span><span class="mtext" id="MathJax-Span-229" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-230"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px;"><span style="position: absolute; clip: rect(3.106em, 1001.99em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-231" style="font-family: STIXGeneral;">km·h</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.388em; left: 2.052em;"><span class="mtext" id="MathJax-Span-232" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>26,14</mtext><mtext> </mtext><msup><mtext>km·h</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-39">\text{26,14} ~\text{km·h}^\text{-1}</script></span>.</span> The warning signal of the garbage truck produces a sound wave with a frequency of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-40-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>332,47</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-233" style="width: 5.097em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.16em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.16em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-234"><span class="mtext" id="MathJax-Span-235" style="font-family: STIXGeneral;">332,47</span><span class="mtext" id="MathJax-Span-236" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-237" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>332,47</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-40">\text{332,47} ~\text{Hz}</script></span>.</span> The person riding in the car hears the sound wave produced by the warning signal of the garbage truck at an apparent frequency of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-41-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>355,04</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-238" style="width: 5.097em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.16em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.16em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-239"><span class="mtext" id="MathJax-Span-240" style="font-family: STIXGeneral;">355,04</span><span class="mtext" id="MathJax-Span-241" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-242" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>355,04</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-41">\text{355,04} ~\text{Hz}</script></span>.</span>
</p>
<p>
Use the above information to determine the following:
</p>
<p>
What is the speed of sound at the prevailing conditions?
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
<ul>
<li>Round your answer to <strong>two decimal places</strong>.</li>
<li>Use the values for any physical constants you might need, as listed <a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">here</a>.</li>
</ul>
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
The speed of sound at the prevailing conditions is <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="340,05" size="10"> <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-42-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><msup><mtext>m&#xB7;s</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-243" style="width: 2.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.345em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1002.35em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-244"><span class="mtext" id="MathJax-Span-245" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-246"><span style="display: inline-block; position: relative; width: 2.111em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1001.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-247" style="font-family: STIXGeneral;">m·s</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 1.408em;"><span class="mtext" id="MathJax-Span-248" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><msup><mtext>m·s</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-42">~\text{m·s}^\text{-1}</script></span>.</span>
<div class="response-type">numeric</div></div></div></div>
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</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id2026-7240">ID is: 2026 Seed is: 7240<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/455789eb-be43-5315-ba8c-57c1a4853176" method="POST">
<span class="worked_example"><h3 class="sv-heading">The Doppler effect: sound waves</h3>
</span><div class="problem">
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/2026/7240/0"><img src="./CAPS-Science-Grade-12-6-Doppler-effect_files/0"></a></div>
<p>
<strong>Mandilakhe</strong> is riding in a taxi, which is traveling at a speed of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-43-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>68,61</mtext><mtext>&#xA0;</mtext><msup><mtext>km&#xB7;h</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-249" style="width: 6.385em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.214em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1005.21em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-250"><span class="mtext" id="MathJax-Span-251" style="font-family: STIXGeneral;">68,61</span><span class="mtext" id="MathJax-Span-252" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-253"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px;"><span style="position: absolute; clip: rect(3.106em, 1001.99em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-254" style="font-family: STIXGeneral;">km·h</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.388em; left: 2.052em;"><span class="mtext" id="MathJax-Span-255" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>68,61</mtext><mtext> </mtext><msup><mtext>km·h</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-43">\text{68,61} ~\text{km·h}^\text{-1}</script></span>,</span> and moving towards the direction as shown in the diagram above.
</p>
<p>
<strong>Bokamoso</strong> is riding in a car, which is traveling at a speed of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-44-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>53,4</mtext><mtext>&#xA0;</mtext><msup><mtext>km&#xB7;h</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-256" style="width: 5.741em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.687em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1004.69em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-257"><span class="mtext" id="MathJax-Span-258" style="font-family: STIXGeneral;">53,4</span><span class="mtext" id="MathJax-Span-259" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-260"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px;"><span style="position: absolute; clip: rect(3.106em, 1001.99em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-261" style="font-family: STIXGeneral;">km·h</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.388em; left: 2.052em;"><span class="mtext" id="MathJax-Span-262" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>53,4</mtext><mtext> </mtext><msup><mtext>km·h</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-44">\text{53,4} ~\text{km·h}^\text{-1}</script></span>,</span> and moving in the same direction as <strong>Mandilakhe</strong>.
</p>
<p>
A firetruck is traveling in the same direction as both <strong>Mandilakhe</strong> and <strong>Bokamoso</strong>, and is ahead of the taxi carrying <strong>Mandilakhe</strong>. The firetruck is traveling at a speed of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-45-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>44,95</mtext><mtext>&#xA0;</mtext><msup><mtext>km&#xB7;h</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-263" style="width: 6.385em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.214em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1005.21em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-264"><span class="mtext" id="MathJax-Span-265" style="font-family: STIXGeneral;">44,95</span><span class="mtext" id="MathJax-Span-266" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-267"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px;"><span style="position: absolute; clip: rect(3.106em, 1001.99em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-268" style="font-family: STIXGeneral;">km·h</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.388em; left: 2.052em;"><span class="mtext" id="MathJax-Span-269" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>44,95</mtext><mtext> </mtext><msup><mtext>km·h</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-45">\text{44,95} ~\text{km·h}^\text{-1}</script></span>.</span>
</p>
<p>
The siren of the firetruck produces a sound wave with a frequency of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-46-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>249,26</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-270" style="width: 5.097em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.16em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.16em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-271"><span class="mtext" id="MathJax-Span-272" style="font-family: STIXGeneral;">249,26</span><span class="mtext" id="MathJax-Span-273" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-274" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>249,26</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-46">\text{249,26} ~\text{Hz}</script></span>.</span>
</p>
<p>
Assume that the speed of sound is <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-47-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>341,65</mtext><mtext>&#xA0;</mtext><msup><mtext>m&#xB7;s</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-275" style="width: 6.209em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.097em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1005.1em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-276"><span class="mtext" id="MathJax-Span-277" style="font-family: STIXGeneral;">341,65</span><span class="mtext" id="MathJax-Span-278" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-279"><span style="display: inline-block; position: relative; width: 2.111em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1001.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-280" style="font-family: STIXGeneral;">m·s</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 1.408em;"><span class="mtext" id="MathJax-Span-281" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.361em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>341,65</mtext><mtext> </mtext><msup><mtext>m·s</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-47">\text{341,65}~\text{m·s}^\text{-1}</script></span>.</span>
</p>
<p>
Use the above information to determine the following:
</p>
<ol>
<li>
<p>
What is the apparent frequency of the sound wave produced by the siren of the firetruck that <strong>Mandilakhe</strong> will hear? <strong>(round your answer to two decimal places)</strong>
</p>
</li>
<li>
<p>
What is the apparent frequency of the sound wave produced by the siren of the firetruck that <strong>Bokamoso</strong> will hear? <strong>(round your answer to two decimal places)</strong>
</p>
</li>
<li>
<p>
Which person will observe the higher apparent frequency for the sound wave produced by the siren of the firetruck?
</p>
</li>
</ol>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<ol>
<li>
<p>
The frequency of the sound wave that <strong>Mandilakhe</strong> will hear is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-48-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mrow class="MJX-TeXAtom-ORD"><mi>L</mi><mo>,</mo><mtext>&#xA0;</mtext><mtext>Mandilakhe</mtext></mrow></msub><mo>&#x2248;</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-282" style="width: 7.146em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.858em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1005.8em, 2.93em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-283"><span class="msubsup" id="MathJax-Span-284"><span style="display: inline-block; position: relative; width: 4.862em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.65em, 4.335em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-285" style="font-family: STIXGeneral; font-style: italic;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.53em;"><span class="texatom" id="MathJax-Span-286"><span class="mrow" id="MathJax-Span-287"><span class="mi" id="MathJax-Span-288" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝐿</span><span class="mo" id="MathJax-Span-289" style="font-size: 70.7%; font-family: STIXGeneral;">,</span><span class="mtext" id="MathJax-Span-290" style="font-size: 70.7%; font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-291" style="font-size: 70.7%; font-family: STIXGeneral;">Mandilakhe</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-292" style="font-family: STIXGeneral; padding-left: 0.296em;">≈</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.354em; border-left: 0px solid; width: 0px; height: 1.289em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mrow class="MJX-TeXAtom-ORD"><mi>L</mi><mo>,</mo><mtext> </mtext><mtext>Mandilakhe</mtext></mrow></msub><mo>≈</mo></math></span></span><script type="math/tex" id="MathJax-Element-48">f_{L,~\text{Mandilakhe}} \approx</script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="253,89" size="10"> <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-49-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-293" style="width: 1.759em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.408em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.41em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-294"><span class="mtext" id="MathJax-Span-295" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-296" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-49">~\text{Hz}</script></span>.</span>
</p>
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<p>
The frequency of the sound wave that <strong>Bokamoso</strong> will hear is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-50-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mrow class="MJX-TeXAtom-ORD"><mi>L</mi><mo>,</mo><mtext>&#xA0;</mtext><mtext>Bokamoso</mtext></mrow></msub><mo>&#x2248;</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-297" style="width: 6.736em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.506em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1005.45em, 2.93em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-298"><span class="msubsup" id="MathJax-Span-299"><span style="display: inline-block; position: relative; width: 4.511em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.65em, 4.335em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-300" style="font-family: STIXGeneral; font-style: italic;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.53em;"><span class="texatom" id="MathJax-Span-301"><span class="mrow" id="MathJax-Span-302"><span class="mi" id="MathJax-Span-303" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝐿</span><span class="mo" id="MathJax-Span-304" style="font-size: 70.7%; font-family: STIXGeneral;">,</span><span class="mtext" id="MathJax-Span-305" style="font-size: 70.7%; font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-306" style="font-size: 70.7%; font-family: STIXGeneral;">Bokamoso</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-307" style="font-family: STIXGeneral; padding-left: 0.296em;">≈</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.354em; border-left: 0px solid; width: 0px; height: 1.289em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mrow class="MJX-TeXAtom-ORD"><mi>L</mi><mo>,</mo><mtext> </mtext><mtext>Bokamoso</mtext></mrow></msub><mo>≈</mo></math></span></span><script type="math/tex" id="MathJax-Element-50">f_{L,~\text{Bokamoso}} \approx</script></span> <input name="question1b" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="250,91" size="10"> <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-51-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-308" style="width: 1.759em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.408em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.41em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-309"><span class="mtext" id="MathJax-Span-310" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-311" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-51">~\text{Hz}</script></span>.</span>
</p>
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<li>
<p>
The person who will observe the higher apparent frequency is <select name="question1c" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0" selected="">Mandilakhe</option><option value="1">Bokamoso</option></select>.
</p>
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</ol>
<div class="response-type">numeric</div><div class="response-type">numeric</div></div></div></div>
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</div></section><section class="sv-section sv-question sv-table"><br><div class="id2026-34">ID is: 2026 Seed is: 34<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/455789eb-be43-5315-ba8c-57c1a4853176" method="POST">
<span class="worked_example"><h3 class="sv-heading">The Doppler effect: sound waves</h3>
</span><div class="problem">
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/2026/34/0"><img src="./CAPS-Science-Grade-12-6-Doppler-effect_files/0(1)"></a></div>
<p>
<strong>Saymore</strong> is riding in a minibus, which is traveling at a speed of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-52-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>56,96</mtext><mtext>&#xA0;</mtext><msup><mtext>km&#xB7;h</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-312" style="width: 6.385em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.214em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1005.21em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-313"><span class="mtext" id="MathJax-Span-314" style="font-family: STIXGeneral;">56,96</span><span class="mtext" id="MathJax-Span-315" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-316"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px;"><span style="position: absolute; clip: rect(3.106em, 1001.99em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-317" style="font-family: STIXGeneral;">km·h</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.388em; left: 2.052em;"><span class="mtext" id="MathJax-Span-318" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>56,96</mtext><mtext> </mtext><msup><mtext>km·h</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-52">\text{56,96} ~\text{km·h}^\text{-1}</script></span>,</span> and moving towards the direction as shown in the diagram above.
</p>
<p>
<strong>Masoabi</strong> is riding in a delivery van, which is traveling at a speed of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-53-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>43,78</mtext><mtext>&#xA0;</mtext><msup><mtext>km&#xB7;h</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-319" style="width: 6.385em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.214em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1005.21em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-320"><span class="mtext" id="MathJax-Span-321" style="font-family: STIXGeneral;">43,78</span><span class="mtext" id="MathJax-Span-322" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-323"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px;"><span style="position: absolute; clip: rect(3.106em, 1001.99em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-324" style="font-family: STIXGeneral;">km·h</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.388em; left: 2.052em;"><span class="mtext" id="MathJax-Span-325" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>43,78</mtext><mtext> </mtext><msup><mtext>km·h</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-53">\text{43,78} ~\text{km·h}^\text{-1}</script></span>,</span> and moving in the same direction as <strong>Saymore</strong>.
</p>
<p>
A mechanical street sweeper is traveling in the same direction as both <strong>Saymore</strong> and <strong>Masoabi</strong>, and is ahead of the minibus carrying <strong>Saymore</strong>. The mechanical street sweeper is traveling at a speed of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-54-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>46,19</mtext><mtext>&#xA0;</mtext><msup><mtext>km&#xB7;h</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-326" style="width: 6.385em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.214em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1005.21em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-327"><span class="mtext" id="MathJax-Span-328" style="font-family: STIXGeneral;">46,19</span><span class="mtext" id="MathJax-Span-329" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-330"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px;"><span style="position: absolute; clip: rect(3.106em, 1001.99em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-331" style="font-family: STIXGeneral;">km·h</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.388em; left: 2.052em;"><span class="mtext" id="MathJax-Span-332" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>46,19</mtext><mtext> </mtext><msup><mtext>km·h</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-54">\text{46,19} ~\text{km·h}^\text{-1}</script></span>.</span>
</p>
<p>
The warning signal of the mechanical street sweeper produces a sound wave with a frequency of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-55-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>364,54</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-333" style="width: 5.097em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.16em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.16em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-334"><span class="mtext" id="MathJax-Span-335" style="font-family: STIXGeneral;">364,54</span><span class="mtext" id="MathJax-Span-336" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-337" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>364,54</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-55">\text{364,54} ~\text{Hz}</script></span>.</span>
</p>
<p>
Assume that the speed of sound is <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-56-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>349,23</mtext><mtext>&#xA0;</mtext><msup><mtext>m&#xB7;s</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-338" style="width: 6.209em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.097em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1005.1em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-339"><span class="mtext" id="MathJax-Span-340" style="font-family: STIXGeneral;">349,23</span><span class="mtext" id="MathJax-Span-341" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-342"><span style="display: inline-block; position: relative; width: 2.111em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1001.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-343" style="font-family: STIXGeneral;">m·s</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 1.408em;"><span class="mtext" id="MathJax-Span-344" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.361em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>349,23</mtext><mtext> </mtext><msup><mtext>m·s</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-56">\text{349,23}~\text{m·s}^\text{-1}</script></span>.</span>
</p>
<p>
Use the above information to determine the following:
</p>
<ol>
<li>
<p>
What is the apparent frequency of the sound wave produced by the warning signal of the mechanical street sweeper that <strong>Saymore</strong> will hear? <strong>(round your answer to two decimal places)</strong>
</p>
</li>
<li>
<p>
What is the apparent frequency of the sound wave produced by the warning signal of the mechanical street sweeper that <strong>Masoabi</strong> will hear? <strong>(round your answer to two decimal places)</strong>
</p>
</li>
<li>
<p>
Which person will observe the higher apparent frequency for the sound wave produced by the warning signal of the mechanical street sweeper?
</p>
</li>
</ol>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<ol>
<li>
<p>
The frequency of the sound wave that <strong>Saymore</strong> will hear is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-57-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mrow class="MJX-TeXAtom-ORD"><mi>L</mi><mo>,</mo><mtext>&#xA0;</mtext><mtext>Saymore</mtext></mrow></msub><mo>&#x2248;</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-345" style="width: 6.092em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.98em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1004.92em, 2.989em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-346"><span class="msubsup" id="MathJax-Span-347"><span style="display: inline-block; position: relative; width: 3.984em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.65em, 4.335em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-348" style="font-family: STIXGeneral; font-style: italic;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.53em;"><span class="texatom" id="MathJax-Span-349"><span class="mrow" id="MathJax-Span-350"><span class="mi" id="MathJax-Span-351" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝐿</span><span class="mo" id="MathJax-Span-352" style="font-size: 70.7%; font-family: STIXGeneral;">,</span><span class="mtext" id="MathJax-Span-353" style="font-size: 70.7%; font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-354" style="font-size: 70.7%; font-family: STIXGeneral;">Saymore</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-355" style="font-family: STIXGeneral; padding-left: 0.296em;">≈</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.425em; border-left: 0px solid; width: 0px; height: 1.361em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mrow class="MJX-TeXAtom-ORD"><mi>L</mi><mo>,</mo><mtext> </mtext><mtext>Saymore</mtext></mrow></msub><mo>≈</mo></math></span></span><script type="math/tex" id="MathJax-Element-57">f_{L,~\text{Saymore}} \approx</script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="367,55" size="10"> <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-58-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-356" style="width: 1.759em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.408em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.41em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-357"><span class="mtext" id="MathJax-Span-358" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-359" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-58">~\text{Hz}</script></span>.</span>
</p>
</li>
<li>
<p>
The frequency of the sound wave that <strong>Masoabi</strong> will hear is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-59-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mrow class="MJX-TeXAtom-ORD"><mi>L</mi><mo>,</mo><mtext>&#xA0;</mtext><mtext>Masoabi</mtext></mrow></msub><mo>&#x2248;</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-360" style="width: 6.033em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.921em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1004.86em, 2.93em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-361"><span class="msubsup" id="MathJax-Span-362"><span style="display: inline-block; position: relative; width: 3.926em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.65em, 4.335em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-363" style="font-family: STIXGeneral; font-style: italic;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.53em;"><span class="texatom" id="MathJax-Span-364"><span class="mrow" id="MathJax-Span-365"><span class="mi" id="MathJax-Span-366" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝐿</span><span class="mo" id="MathJax-Span-367" style="font-size: 70.7%; font-family: STIXGeneral;">,</span><span class="mtext" id="MathJax-Span-368" style="font-size: 70.7%; font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-369" style="font-size: 70.7%; font-family: STIXGeneral;">Masoabi</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-370" style="font-family: STIXGeneral; padding-left: 0.296em;">≈</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.354em; border-left: 0px solid; width: 0px; height: 1.289em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mrow class="MJX-TeXAtom-ORD"><mi>L</mi><mo>,</mo><mtext> </mtext><mtext>Masoabi</mtext></mrow></msub><mo>≈</mo></math></span></span><script type="math/tex" id="MathJax-Element-59">f_{L,~\text{Masoabi}} \approx</script></span> <input name="question1b" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="363,87" size="10"> <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-60-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-371" style="width: 1.759em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.408em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.41em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-372"><span class="mtext" id="MathJax-Span-373" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-374" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-60">~\text{Hz}</script></span>.</span>
</p>
</li>
<li>
<p>
The person who will observe the higher apparent frequency is <select name="question1c" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0" selected="">Saymore</option><option value="1">Masoabi</option></select>.
</p>
</li>
</ol>
<div class="response-type">numeric</div><div class="response-type">numeric</div></div></div></div>
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</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id2016-675">ID is: 2016 Seed is: 675<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/455789eb-be43-5315-ba8c-57c1a4853176" method="POST">
<span class="worked_example"><h3 class="sv-heading">The Doppler effect: sound waves</h3>
</span><div class="problem">
<p>
A person is riding in a tram which is travelling at a certain speed. Travelling in the opposite direction to the tram is a police motorcycle, approaching at a speed of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-61-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>105,21</mtext><mtext>&#xA0;</mtext><msup><mtext>km&#xB7;h</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-375" style="width: 6.97em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.682em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1005.68em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-376"><span class="mtext" id="MathJax-Span-377" style="font-family: STIXGeneral;">105,21</span><span class="mtext" id="MathJax-Span-378" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-379"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px;"><span style="position: absolute; clip: rect(3.106em, 1001.99em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-380" style="font-family: STIXGeneral;">km·h</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.388em; left: 2.052em;"><span class="mtext" id="MathJax-Span-381" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>105,21</mtext><mtext> </mtext><msup><mtext>km·h</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-61">\text{105,21} ~\text{km·h}^\text{-1}</script></span>.</span> The siren of the police motorcycle produces a sound wave with a frequency of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-62-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>493,91</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-382" style="width: 5.097em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.16em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.16em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-383"><span class="mtext" id="MathJax-Span-384" style="font-family: STIXGeneral;">493,91</span><span class="mtext" id="MathJax-Span-385" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-386" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>493,91</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-62">\text{493,91} ~\text{Hz}</script></span>.</span> The person riding in the tram hears the sound wave produced by the siren of the police motorcycle at an apparent frequency of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-63-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>554,92</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-387" style="width: 5.097em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.16em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.16em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-388"><span class="mtext" id="MathJax-Span-389" style="font-family: STIXGeneral;">554,92</span><span class="mtext" id="MathJax-Span-390" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-391" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>554,92</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-63">\text{554,92} ~\text{Hz}</script></span>.</span> Assume that the speed of sound is <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-64-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>343</mtext><mtext>&#xA0;</mtext><msup><mtext>m&#xB7;s</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-392" style="width: 4.745em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.867em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1003.87em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-393"><span class="mtext" id="MathJax-Span-394" style="font-family: STIXGeneral;">343</span><span class="mtext" id="MathJax-Span-395" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-396"><span style="display: inline-block; position: relative; width: 2.111em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1001.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-397" style="font-family: STIXGeneral;">m·s</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 1.408em;"><span class="mtext" id="MathJax-Span-398" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>343</mtext><mtext> </mtext><msup><mtext>m·s</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-64">\text{343}~\text{m·s}^\text{-1}</script></span>.</span>
</p>
<p>
Use the above information to determine the following:
</p>
<p>
What is the speed of the tram in which the person is travelling?
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
<ul>
<li>Round your answer to <strong>two decimal places</strong>.</li>
<li>Use the values for any physical constants you might need, as listed <a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">here</a>.</li>
</ul>
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
The speed of the tram in which the person is traveling is <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="34,32" size="10"> <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-65-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><msup><mtext>km&#xB7;h</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-399" style="width: 3.574em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.93em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1002.93em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-400"><span class="mtext" id="MathJax-Span-401" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-402"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px;"><span style="position: absolute; clip: rect(3.106em, 1001.99em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-403" style="font-family: STIXGeneral;">km·h</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.388em; left: 2.052em;"><span class="mtext" id="MathJax-Span-404" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><msup><mtext>km·h</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-65">~\text{km·h}^\text{-1}</script></span>.</span>
<div class="response-type">numeric</div></div></div></div>
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</div></section><section class="sv-section sv-question sv-table"><br><div class="id2016-5089">ID is: 2016 Seed is: 5089<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/455789eb-be43-5315-ba8c-57c1a4853176" method="POST">
<span class="worked_example"><h3 class="sv-heading">The Doppler effect: sound waves</h3>
</span><div class="problem">
<p>
A person is riding in a bus which is travelling at a certain speed. Travelling in the opposite direction to the bus is a firetruck, approaching at a speed of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-66-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>95,72</mtext><mtext>&#xA0;</mtext><msup><mtext>km&#xB7;h</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-405" style="width: 6.385em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.214em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1005.21em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-406"><span class="mtext" id="MathJax-Span-407" style="font-family: STIXGeneral;">95,72</span><span class="mtext" id="MathJax-Span-408" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-409"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px;"><span style="position: absolute; clip: rect(3.106em, 1001.99em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-410" style="font-family: STIXGeneral;">km·h</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.388em; left: 2.052em;"><span class="mtext" id="MathJax-Span-411" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>95,72</mtext><mtext> </mtext><msup><mtext>km·h</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-66">\text{95,72} ~\text{km·h}^\text{-1}</script></span>.</span> The siren of the firetruck produces a sound wave with a frequency of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-67-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>312,77</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-412" style="width: 5.097em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.16em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.16em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-413"><span class="mtext" id="MathJax-Span-414" style="font-family: STIXGeneral;">312,77</span><span class="mtext" id="MathJax-Span-415" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-416" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>312,77</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-67">\text{312,77} ~\text{Hz}</script></span>.</span> The person riding in the bus hears the sound wave produced by the siren of the firetruck at an apparent frequency of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-68-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>351,29</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-417" style="width: 5.097em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.16em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.16em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-418"><span class="mtext" id="MathJax-Span-419" style="font-family: STIXGeneral;">351,29</span><span class="mtext" id="MathJax-Span-420" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-421" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>351,29</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-68">\text{351,29} ~\text{Hz}</script></span>.</span> Assume that the speed of sound is <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-69-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>340</mtext><mtext>&#xA0;</mtext><msup><mtext>m&#xB7;s</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-422" style="width: 4.745em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.867em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1003.87em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-423"><span class="mtext" id="MathJax-Span-424" style="font-family: STIXGeneral;">340</span><span class="mtext" id="MathJax-Span-425" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-426"><span style="display: inline-block; position: relative; width: 2.111em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1001.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-427" style="font-family: STIXGeneral;">m·s</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 1.408em;"><span class="mtext" id="MathJax-Span-428" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>340</mtext><mtext> </mtext><msup><mtext>m·s</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-69">\text{340}~\text{m·s}^\text{-1}</script></span>.</span>
</p>
<p>
Use the above information to determine the following:
</p>
<p>
What is the speed of the bus in which the person is travelling?
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
<ul>
<li>Round your answer to <strong>two decimal places</strong>.</li>
<li>Use the values for any physical constants you might need, as listed <a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">here</a>.</li>
</ul>
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
The speed of the bus in which the person is traveling is <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="43,24" size="10"> <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-70-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><msup><mtext>km&#xB7;h</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-429" style="width: 3.574em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.93em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1002.93em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-430"><span class="mtext" id="MathJax-Span-431" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-432"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px;"><span style="position: absolute; clip: rect(3.106em, 1001.99em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-433" style="font-family: STIXGeneral;">km·h</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.388em; left: 2.052em;"><span class="mtext" id="MathJax-Span-434" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><msup><mtext>km·h</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-70">~\text{km·h}^\text{-1}</script></span>.</span>
<div class="response-type">numeric</div></div></div></div>
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</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id2028-8170">ID is: 2028 Seed is: 8170<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/455789eb-be43-5315-ba8c-57c1a4853176" method="POST">
<span class="worked_example"><h3 class="sv-heading">The Doppler effect: sound waves</h3>
</span><div class="problem">
<p>
The sound wave produced by the siren of a police van has a frequency of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-71-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><mtext>622</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-435" style="width: 3.867em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.165em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.16em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-436"><span class="mtext" id="MathJax-Span-437" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-438" style="font-family: STIXGeneral;">622</span><span class="mtext" id="MathJax-Span-439" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-440" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><mtext>622</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-71">~\text{622}~\text{Hz}</script></span>.</span> You are standing at an ice cream kiosk. The police van is moving away (receding) from you at a speed of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-72-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>64</mtext><mtext>&#xA0;</mtext><msup><mtext>km&#xB7;h</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-441" style="width: 4.804em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.926em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1003.93em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-442"><span class="mtext" id="MathJax-Span-443" style="font-family: STIXGeneral;">64</span><span class="mtext" id="MathJax-Span-444" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-445"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px;"><span style="position: absolute; clip: rect(3.106em, 1001.99em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-446" style="font-family: STIXGeneral;">km·h</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.388em; left: 2.052em;"><span class="mtext" id="MathJax-Span-447" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>64</mtext><mtext> </mtext><msup><mtext>km·h</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-72">\text{64} ~\text{km·h}^\text{-1}</script></span>.</span> Assume that the speed of sound is <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-73-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>348</mtext><mtext>&#xA0;</mtext><msup><mtext>m&#xB7;s</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-448" style="width: 4.745em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.867em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1003.87em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-449"><span class="mtext" id="MathJax-Span-450" style="font-family: STIXGeneral;">348</span><span class="mtext" id="MathJax-Span-451" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-452"><span style="display: inline-block; position: relative; width: 2.111em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1001.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-453" style="font-family: STIXGeneral;">m·s</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 1.408em;"><span class="mtext" id="MathJax-Span-454" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>348</mtext><mtext> </mtext><msup><mtext>m·s</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-73">\text{348}~\text{m·s}^\text{-1}</script></span>.</span>
</p>
<p>
Use the above information to determine the following:
</p>
<p>
What is the apparent frequency of the sound wave that you will hear from the siren of the receding police van, or <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-74-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><msub><mi>f</mi><mi>L</mi></msub></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-455" style="width: 1.642em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.35em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.35em, 2.872em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-456"><span class="mtext" id="MathJax-Span-457" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-458"><span style="display: inline-block; position: relative; width: 1.115em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.65em, 4.335em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-459" style="font-family: STIXGeneral; font-style: italic;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.53em;"><span class="mi" id="MathJax-Span-460" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝐿</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><msub><mi>f</mi><mi>L</mi></msub></math></span></span><script type="math/tex" id="MathJax-Element-74">~f_L</script></span>?</span>
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
<ul>
<li>Round your answer to <strong>two decimal places.</strong></li>
<li>Use the values for any physical constants you might need, as listed <a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">here</a>.</li>
</ul>
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
The frequency of the siren you hear is <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="591,77" size="10"> <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-75-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-461" style="width: 1.759em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.408em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.41em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-462"><span class="mtext" id="MathJax-Span-463" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-464" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-75">~\text{Hz}</script></span>.</span>
<div class="response-type">numeric</div></div></div></div>
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</div></section><section class="sv-section sv-question sv-table"><br><div class="id2028-5557">ID is: 2028 Seed is: 5557<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/455789eb-be43-5315-ba8c-57c1a4853176" method="POST">
<span class="worked_example"><h3 class="sv-heading">The Doppler effect: sound waves</h3>
</span><div class="problem">
<p>
The sound wave produced by the siren of a police van has a frequency of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-76-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><mtext>213</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-465" style="width: 3.867em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.165em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.16em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-466"><span class="mtext" id="MathJax-Span-467" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-468" style="font-family: STIXGeneral;">213</span><span class="mtext" id="MathJax-Span-469" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-470" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><mtext>213</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-76">~\text{213}~\text{Hz}</script></span>.</span> You are standing at the side of the road. The police van is moving away (receding) from you at a speed of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-77-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>80</mtext><mtext>&#xA0;</mtext><msup><mtext>km&#xB7;h</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-471" style="width: 4.804em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.926em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1003.93em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-472"><span class="mtext" id="MathJax-Span-473" style="font-family: STIXGeneral;">80</span><span class="mtext" id="MathJax-Span-474" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-475"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px;"><span style="position: absolute; clip: rect(3.106em, 1001.99em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-476" style="font-family: STIXGeneral;">km·h</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.388em; left: 2.052em;"><span class="mtext" id="MathJax-Span-477" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>80</mtext><mtext> </mtext><msup><mtext>km·h</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-77">\text{80} ~\text{km·h}^\text{-1}</script></span>.</span> Assume that the speed of sound is <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-78-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>340</mtext><mtext>&#xA0;</mtext><msup><mtext>m&#xB7;s</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-478" style="width: 4.745em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.867em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1003.87em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-479"><span class="mtext" id="MathJax-Span-480" style="font-family: STIXGeneral;">340</span><span class="mtext" id="MathJax-Span-481" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-482"><span style="display: inline-block; position: relative; width: 2.111em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1001.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-483" style="font-family: STIXGeneral;">m·s</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 1.408em;"><span class="mtext" id="MathJax-Span-484" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>340</mtext><mtext> </mtext><msup><mtext>m·s</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-78">\text{340}~\text{m·s}^\text{-1}</script></span>.</span>
</p>
<p>
Use the above information to determine the following:
</p>
<p>
What is the apparent frequency of the sound wave that you will hear from the siren of the receding police van, or <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-79-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><msub><mi>f</mi><mi>L</mi></msub></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-485" style="width: 1.642em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.35em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.35em, 2.872em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-486"><span class="mtext" id="MathJax-Span-487" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-488"><span style="display: inline-block; position: relative; width: 1.115em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.65em, 4.335em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-489" style="font-family: STIXGeneral; font-style: italic;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.53em;"><span class="mi" id="MathJax-Span-490" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝐿</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><msub><mi>f</mi><mi>L</mi></msub></math></span></span><script type="math/tex" id="MathJax-Element-79">~f_L</script></span>?</span>
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
<ul>
<li>Round your answer to <strong>two decimal places.</strong></li>
<li>Use the values for any physical constants you might need, as listed <a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">here</a>.</li>
</ul>
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
The frequency of the siren you hear is <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="199,93" size="10"> <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-80-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-491" style="width: 1.759em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.408em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.41em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-492"><span class="mtext" id="MathJax-Span-493" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-494" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-80">~\text{Hz}</script></span>.</span>
<div class="response-type">numeric</div></div></div></div>
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</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id2022-6974">ID is: 2022 Seed is: 6974<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/455789eb-be43-5315-ba8c-57c1a4853176" method="POST">
<span class="worked_example"><h3 class="sv-heading">The Doppler effect: sound waves</h3>
</span><div class="problem">
<p>
The siren of a garbage truck produces a sound wave with a frequency of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-81-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>347</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-495" style="width: 3.574em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.93em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.93em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-496"><span class="mtext" id="MathJax-Span-497" style="font-family: STIXGeneral;">347</span><span class="mtext" id="MathJax-Span-498" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-499" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>347</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-81">\text{347}~\text{Hz}</script></span>.</span> You are standing at a hot dog stand. The garbage truck is moving away from you at a certain speed. The apparent frequency of the sound wave you hear is <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-82-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>334</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-500" style="width: 3.574em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.93em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.93em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-501"><span class="mtext" id="MathJax-Span-502" style="font-family: STIXGeneral;">334</span><span class="mtext" id="MathJax-Span-503" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-504" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>334</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-82">\text{334}~\text{Hz}</script></span>.</span> Assume that the speed of sound is <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-83-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>340,0</mtext><mtext>&#xA0;</mtext><msup><mtext>m&#xB7;s</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-505" style="width: 5.682em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.628em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1004.63em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-506"><span class="mtext" id="MathJax-Span-507" style="font-family: STIXGeneral;">340,0</span><span class="mtext" id="MathJax-Span-508" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-509"><span style="display: inline-block; position: relative; width: 2.111em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1001.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-510" style="font-family: STIXGeneral;">m·s</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 1.408em;"><span class="mtext" id="MathJax-Span-511" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.361em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>340,0</mtext><mtext> </mtext><msup><mtext>m·s</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-83">\text{340,0}~\text{m·s}^\text{-1}</script></span>.</span>
</p>
<p>
Use the above information to determine the following:
</p>
<p>
What is the speed of the receding garbage truck, or <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-84-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><msub><mi>v</mi><mi>S</mi></msub></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-512" style="width: 1.584em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.291em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.876em, 1001.29em, 2.872em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-513"><span class="mtext" id="MathJax-Span-514" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-515"><span style="display: inline-block; position: relative; width: 1.057em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1000.47em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-516" style="font-family: STIXGeneral; font-style: italic;">𝑣</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.53em;"><span class="mi" id="MathJax-Span-517" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑆<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><msub><mi>v</mi><mi>S</mi></msub></math></span></span><script type="math/tex" id="MathJax-Element-84">~v_S</script></span>?</span>
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
<ul>
<li>Round your answer to <strong>two decimal places</strong>.</li>
<li>Use the values for any physical constants you might need, as listed <a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">here</a>.</li>
</ul>
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
The speed of the garbage truck is <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="47,64" size="10"> <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-85-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><msup><mtext>km&#xB7;h</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-518" style="width: 3.574em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.93em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1002.93em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-519"><span class="mtext" id="MathJax-Span-520" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-521"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px;"><span style="position: absolute; clip: rect(3.106em, 1001.99em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-522" style="font-family: STIXGeneral;">km·h</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.388em; left: 2.052em;"><span class="mtext" id="MathJax-Span-523" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><msup><mtext>km·h</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-85">~\text{km·h}^\text{-1}</script></span>.</span>
<div class="response-type">one-of<div class="response-subtype">type(numeric.abserror(0.01))</div></div></div></div></div>
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</div></section><section class="sv-section sv-question sv-table"><br><div class="id2022-4684">ID is: 2022 Seed is: 4684<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/455789eb-be43-5315-ba8c-57c1a4853176" method="POST">
<span class="worked_example"><h3 class="sv-heading">The Doppler effect: sound waves</h3>
</span><div class="problem">
<p>
The siren of a garbage truck produces a sound wave with a frequency of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-86-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>762</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-524" style="width: 3.574em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.93em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.93em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-525"><span class="mtext" id="MathJax-Span-526" style="font-family: STIXGeneral;">762</span><span class="mtext" id="MathJax-Span-527" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-528" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>762</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-86">\text{762}~\text{Hz}</script></span>.</span> You are standing at a bus stop shelter. The garbage truck is moving away from you at a certain speed. The apparent frequency of the sound wave you hear is <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-87-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>731</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-529" style="width: 3.574em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.93em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.93em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-530"><span class="mtext" id="MathJax-Span-531" style="font-family: STIXGeneral;">731</span><span class="mtext" id="MathJax-Span-532" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-533" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>731</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-87">\text{731}~\text{Hz}</script></span>.</span> Assume that the speed of sound is <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-88-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>335,9</mtext><mtext>&#xA0;</mtext><msup><mtext>m&#xB7;s</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-534" style="width: 5.682em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.628em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1004.63em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-535"><span class="mtext" id="MathJax-Span-536" style="font-family: STIXGeneral;">335,9</span><span class="mtext" id="MathJax-Span-537" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-538"><span style="display: inline-block; position: relative; width: 2.111em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1001.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-539" style="font-family: STIXGeneral;">m·s</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 1.408em;"><span class="mtext" id="MathJax-Span-540" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.361em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>335,9</mtext><mtext> </mtext><msup><mtext>m·s</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-88">\text{335,9}~\text{m·s}^\text{-1}</script></span>.</span>
</p>
<p>
Use the above information to determine the following:
</p>
<p>
What is the speed of the receding garbage truck, or <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-89-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><msub><mi>v</mi><mi>S</mi></msub></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-541" style="width: 1.584em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.291em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.876em, 1001.29em, 2.872em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-542"><span class="mtext" id="MathJax-Span-543" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-544"><span style="display: inline-block; position: relative; width: 1.057em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1000.47em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-545" style="font-family: STIXGeneral; font-style: italic;">𝑣</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.53em;"><span class="mi" id="MathJax-Span-546" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑆<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><msub><mi>v</mi><mi>S</mi></msub></math></span></span><script type="math/tex" id="MathJax-Element-89">~v_S</script></span>?</span>
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
<ul>
<li>Round your answer to <strong>two decimal places</strong>.</li>
<li>Use the values for any physical constants you might need, as listed <a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">here</a>.</li>
</ul>
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
The speed of the garbage truck is <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="51,28" size="10"> <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-90-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><msup><mtext>km&#xB7;h</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-547" style="width: 3.574em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.93em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1002.93em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-548"><span class="mtext" id="MathJax-Span-549" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-550"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px;"><span style="position: absolute; clip: rect(3.106em, 1001.99em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-551" style="font-family: STIXGeneral;">km·h</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.388em; left: 2.052em;"><span class="mtext" id="MathJax-Span-552" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><msup><mtext>km·h</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-90">~\text{km·h}^\text{-1}</script></span>.</span>
<div class="response-type">one-of<div class="response-subtype">type(numeric.abserror(0.01))</div></div></div></div></div>
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</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id2032-4487">ID is: 2032 Seed is: 4487<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/455789eb-be43-5315-ba8c-57c1a4853176" method="POST">
<span class="worked_example"><h3 class="sv-heading">The Doppler effect: sound waves</h3>
</span><div class="problem">
<p>
The siren of a police van produces a sound wave with a frequency of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-91-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><mtext>442</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-553" style="width: 3.867em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.165em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.16em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-554"><span class="mtext" id="MathJax-Span-555" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-556" style="font-family: STIXGeneral;">442</span><span class="mtext" id="MathJax-Span-557" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-558" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><mtext>442</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-91">~\text{442}~\text{Hz}</script></span>.</span> You are standing at a hot dog stand. The police van is moving away from you at a speed of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-92-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>68</mtext><mtext>&#xA0;</mtext><msup><mtext>km&#xB7;h</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-559" style="width: 4.804em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.926em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1003.93em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-560"><span class="mtext" id="MathJax-Span-561" style="font-family: STIXGeneral;">68</span><span class="mtext" id="MathJax-Span-562" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-563"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px;"><span style="position: absolute; clip: rect(3.106em, 1001.99em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-564" style="font-family: STIXGeneral;">km·h</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.388em; left: 2.052em;"><span class="mtext" id="MathJax-Span-565" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>68</mtext><mtext> </mtext><msup><mtext>km·h</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-92">\text{68} ~\text{km·h}^\text{-1}</script></span>.</span> The apparent frequency of the sound wave you hear is <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-93-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><mtext>418</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-566" style="width: 3.867em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.165em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.16em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-567"><span class="mtext" id="MathJax-Span-568" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-569" style="font-family: STIXGeneral;">418</span><span class="mtext" id="MathJax-Span-570" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-571" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><mtext>418</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-93">~\text{418}~\text{Hz}</script></span>.</span>
</p>
<p>
Use the above information to determine the following:
</p>
<p>
What is the speed of the sound wave produced by the siren of the police van under these conditions, or <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-94-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><mi>v</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-572" style="width: 0.94em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.764em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.876em, 1000.76em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-573"><span class="mtext" id="MathJax-Span-574" style="font-family: STIXGeneral;"> </span><span class="mi" id="MathJax-Span-575" style="font-family: STIXGeneral; font-style: italic;">𝑣</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><mi>v</mi></math></span></span><script type="math/tex" id="MathJax-Element-94">~v</script></span>?</span>
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
<ul>
<li>Round your answer to <strong>two decimal places</strong>.</li>
<li>Use the values for any physical constants you might need, as listed <a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">here</a>.</li>
</ul>
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
The speed of the sound wave is <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="328,98" size="10"> <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-95-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><msup><mtext>m&#xB7;s</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-576" style="width: 2.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.345em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1002.35em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-577"><span class="mtext" id="MathJax-Span-578" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-579"><span style="display: inline-block; position: relative; width: 2.111em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1001.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-580" style="font-family: STIXGeneral;">m·s</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 1.408em;"><span class="mtext" id="MathJax-Span-581" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><msup><mtext>m·s</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-95">~\text{m·s}^\text{-1}</script></span>.</span>
<div class="response-type">numeric</div></div></div></div>
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</div></section><section class="sv-section sv-question sv-table"><br><div class="id2032-9660">ID is: 2032 Seed is: 9660<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/455789eb-be43-5315-ba8c-57c1a4853176" method="POST">
<span class="worked_example"><h3 class="sv-heading">The Doppler effect: sound waves</h3>
</span><div class="problem">
<p>
The siren of an ambulance produces a sound wave with a frequency of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-96-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><mtext>408</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-582" style="width: 3.867em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.165em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.16em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-583"><span class="mtext" id="MathJax-Span-584" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-585" style="font-family: STIXGeneral;">408</span><span class="mtext" id="MathJax-Span-586" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-587" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><mtext>408</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-96">~\text{408}~\text{Hz}</script></span>.</span> You are standing at the side of the road. The ambulance is moving away from you at a speed of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-97-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>85</mtext><mtext>&#xA0;</mtext><msup><mtext>km&#xB7;h</mtext><mtext>-1</mtext></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-588" style="width: 4.804em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.926em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1003.93em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-589"><span class="mtext" id="MathJax-Span-590" style="font-family: STIXGeneral;">85</span><span class="mtext" id="MathJax-Span-591" style="font-family: STIXGeneral;"> </span><span class="msubsup" id="MathJax-Span-592"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px;"><span style="position: absolute; clip: rect(3.106em, 1001.99em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mtext" id="MathJax-Span-593" style="font-family: STIXGeneral;">km·h</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.388em; left: 2.052em;"><span class="mtext" id="MathJax-Span-594" style="font-size: 70.7%; font-family: STIXGeneral;">-1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>85</mtext><mtext> </mtext><msup><mtext>km·h</mtext><mtext>-1</mtext></msup></math></span></span><script type="math/tex" id="MathJax-Element-97">\text{85} ~\text{km·h}^\text{-1}</script></span>.</span> The apparent frequency of the sound wave you hear is <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-98-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><mtext>381</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-595" style="width: 3.867em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.165em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.16em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-596"><span class="mtext" id="MathJax-Span-597" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-598" style="font-family: STIXGeneral;">381</span><span class="mtext" id="MathJax-Span-599" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-600" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><mtext>381</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-98">~\text{381}~\text{Hz}</script></span>.</span>
</p>
<p>
Use the above information to determine the following:
</p>
<p>
What is the speed of the sound wave produced by the siren of the ambulance under these conditions, or <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-99-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&#xA0;</mtext><mi>v</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-601" style="width: 0.94em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.764em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.876em, 1000.76em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-602"><span class="mtext" id="MathJax-Span-603" style="font-family: STIXGeneral;"> </span><span class="mi" id="MathJax-Span-604" style="font-family: STIXGeneral; font-style: italic;">𝑣</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><mi>v</mi></math></span></span><script type="math/tex" id="MathJax-Element-99">~v</script></span>?</span>
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
<ul>
<li>Round your answer to <strong>two decimal places</strong>.</li>
<li>Use the values for any physical constants you might need, as listed <a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">here</a>.</li>
</ul>
</div>