Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 12 - Sound - Problems - Page 356: 59

Answer

The bat hears a sound frequency of 31.1 kHz

Work Step by Step

This is a situation with two Doppler shifts. First, we can find the frequency detected at the wall, which is a stationary object. $f' = \frac{f}{(1-\frac{v_{source}}{v_{snd}})}$ $f' = \frac{30.0~kHz}{(1-\frac{6.0~m/s}{343~m/s}~)}$ $f' = 30.53~kHz$ Now we can find the frequency detected by the bat. $f'' = (1+\frac{v_{obs}}{v_{snd}})~f'$ $f'' = (1+\frac{6.0~m/s}{343~m/s})~(30.53~kHz)$ $f'' = 31.1~kHz$ The bat hears a sound frequency of 31.1 kHz.
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