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Q17.4-30PE

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College Physics (Urone)
Found in: Page 629
College Physics (Urone)

College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

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Short Answer

(a) What frequency is received by a person watching an oncoming ambulance moving at \(110\;{\rm{km/h}}\)and emitting a steady \(800\;{\rm{Hz}}\) sound from its siren? The speed of sound on this day is \(345\;{\rm{m/s}}\). (b) What frequency does she receive after the ambulance has passed?

(a) The apparent frequency is \(877.58\;{\rm{Hz}}\).

(b) The apparent frequency is \(735.01\;{\rm{Hz}}\).

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Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

The Concept of Apparent Frequency

The apparent frequency to a listener changes depending the sound source is moving away or toward the listener.

Given Data

The frequency is \(f = 800\;{\rm{Hz}}\).

The speed of the ambulance is \({v_s} = 100\;{\rm{km/h}} = 30.5\;{\rm{m/s}}\).

The speed of sound is \(v = 345\;{\rm{m/s}}\).

The speed of the listener is zero.

 Calculation of the frequency of the oncoming ambulance

(a)

The Doppler Effect tells the apparent frequency is,

\(f' = f\left( {\frac{{v - {v_o}}}{{v - {v_s}}}} \right)\)

Now, the apparent frequency is,

\(\begin{array}{c}f' = 800\left( {\frac{{345 - 0}}{{345 - 30.5}}} \right)\\ = 800 \times \frac{{690}}{{629}}\\ = 877.58\;{\rm{Hz}}\end{array}\)

Hence, the apparent frequency is \(877.58\;{\rm{Hz}}\) .

Calculation of the frequency of the passing away ambulance

(b)

Now, the apparent frequency of the passing away ambulance is,

\(\begin{array}{c}f'' = 800\left( {\frac{{345 - 0}}{{345 - \left( { - 30.5} \right)}}} \right)\\ = 800 \times \frac{{690}}{{751}}\\ = 735.01\;{\rm{Hz}}\end{array}\)

Hence, the apparent frequency is \(735.01\;{\rm{Hz}}\) .

Most popular questions for Physics Textbooks

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