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Question

When a source of sound of frequency f crosses a stationary observer with a speed vS(<< speed of sound v), the apparent change in frequency f is given by:

A
2fvsv
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B
2fvvs
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C
fvsv
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D
2fvvs
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Solution

The correct option is B 2fvsv
Concept: When the source approaches the observer then there will be a frequency and when the source passes by the observer then there will be another frequency.
Let, the former frequency is f1 and latter frequency is f2
then Δf=f1f2
or,Δf=f(vvvs)f(vv+vs)
or,Δf=f(1vsv)1f(1+vsv)1
or,Δf=f(1+vsv)f(1vsv) [Using binomial expansion]
or,Δf=f(2vsv)
or,Δf=2fvsv

The correct answer is OptionA:2fvsv

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