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Q.

A motor cyclist is moving away from a stationary observer towards a cliff with a speed v. Velocity of sound in still air is v0. Then beat frequency heard by the observer is [ The motor cyclist is blowing horn at frequency f0 ]

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a

f0vv0

b

f0v0v0

c

2f0vv0(v02-v2)

d

2f0v(v0+v0)

answer is C.

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Detailed Solution

f1= Apparent frequency of sound directly coming from motorcyclist =f0(1+v/v0)f2= Apparent frequency of sound wave reflected from the cliff =f0(1-v/v0)∴Beat frequency =f2-f1=f0(1-v/v0)-f0(1+v/v0)=2f0vv0(v02-v2)
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