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A bat at rest sends out ultrasonic sound waves at 52.5 kHz and receives them returned...

A bat at rest sends out ultrasonic sound waves at 52.5 kHz and receives them returned from an object moving directly away from it at 33.5 m/s . What is the received sound frequency?

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Answer #1

there are two basic steps to go:

At first, the bat is the source at rest, and the object is moving away from the bat. Thus we utilize the moving observer formula for the sound. Additionally, the formula uses subtraction as the sound is moving away.
f' = f [(v+uo)/(v)]

f’ = 52.5kHz*[(343-33.5) / (343)]

f’ = 47.37 kHz

Secondly, we again have to use the Doppler effect. The bat now is a stationary observer, but the object is moving source. Thus we utilize the moving source formula using addition.

f’=f[(v)/(v-uo)]

f’ = 47.37kHz*[(343) / (343+33.5)

f’=43.15 kHz

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