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: 57

Answer

The received sound frequency is 42.6 kHz

Work Step by Step

This is a situation with two Doppler shifts. First, we can find the frequency received by the moving object; $f' = (1-\frac{v_{obs}}{v_{snd}})~f$ $f' = (1-\frac{27.5~m/s}{343~m/s})~(50.0~kHz)$ $f' = 45.99~kHz$ Now we can find the frequency detected by the bat; $f'' = \frac{f'}{(1+\frac{v_{source}}{v_{snd}})}$ $f'' = \frac{45.99~kHz}{(1+\frac{27.5~m/s}{343~m/s}~)}$ $f'' = 42.6~kHz$ The received sound frequency is 42.6 kHz.
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