College Physics (4th Edition)

Published by McGraw-Hill Education
ISBN 10: 0073512141
ISBN 13: 978-0-07351-214-3

Chapter 12 - Problems - Page 466: 72


The beat frequency is $3201~Hz$

Work Step by Step

Let $v$ be the speed of sound in the air and let $v_b$ be the speed of the bat. To find the frequency received by the wall, we can use the equation for the Doppler effect when the source is approaching: $f_o = \left(\frac{v}{v-v_b}\right)~f$ $f_o = \left(\frac{343~m/s}{343~m/s-15~m/s}\right)~(35,000~Hz)$ $f_o = 36,600.6~Hz$ To find the reflected frequency, we can let $f_o$ be the sound source and use the equation for the Doppler effect when the observer is approaching: $f_r = \left(\frac{v+v_b}{v}\right)~f_o$ $f_r = \left(\frac{343~m/s+15~m/s}{343~m/s}\right)~(36,600.6~Hz)$ $f_r = 38,201~Hz$ The beat frequency is the difference between the emitted frequency and the reflected frequency. We can find the frequency difference: $38,201~Hz - 35,000~Hz = 3201~Hz$ The beat frequency is $3201~Hz$
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