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Question

A police car moving at 22 m/s chases a motorcyclist. The policeman sounds his horn at 176 Hz, while both of them move towards a stationary siren of frequency 165Hz. Calculate the speed of the motorcycle, if it is given that he does not observe any beats :

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A
33m/s
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B
22m/s
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C
zero
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D
11m/s
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Solution

The correct option is B 22m/s
Let fh and fs be the frequencies of the horn and siren respectively heard by the motorcycle man.
Given: fh=176Hzfs=165Hzvpolicecar=22m/s
Doppler effect for police car and motorcycle:
fh=fh[vsoundvmanvsoundvpolicecar] =176[340v34022] ............(1)

Doppler effect for siren and motorcycle:
fs=fs[vsound+vmanvsound] =165[340+v340] ............(2)
As the motorcycle man doesn't hear any beat, i.e fh=fs
176[340v318]=165[340+v340]
v=22.3m/s22m/s

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