Question

A bat at rest sends out ultrasonic sound waves at 52.0 kHz and receives them returned from an object moving directly away from it at 15.0 m/s .

What is the received sound frequency?

Answer 1

Using doppler's effect:

frequency received by insect will be, when Source is stationary and observer is moving away from source.

f1 = f0*(V - Vo)/V

f0 = 52 kHz

V = Speed of Sound = 340 m/sec

Vo = speed of Object = 15.0 m/sec

f1 = 52*(340 - 15)/(340) = 49.71 kHz

Now frequency reflected by insect will be when Source is moving away from stationary object

f2 = f1*(V)/(V + Vo)

Using above value of f1

f2 = 49.71*(340)/(340 + 15) = 47.61 kHz

f2 = frequency received by bat = 47.61 kHz

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