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Question

When a train approaches a stationary observer, the apparent frequency of the whistle is n and when the same train recedes away from the observer, the apparent frequency is n′′. Then, the apparent frequency n when the observer moves with the train is :

A
n=nn′′
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B
n=n+n′′2
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C
n=2nn′′nn′′
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D
n=2nn′′n+n′′
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Solution

The correct option is D n=2nn′′n+n′′
When train approaches stationery observer, the apparent frequency n=vnvvs and when the train recedes away train the observer, the apparent frequency n′′=vnv+vs
or nn=1vsv...(i)
and nn=1+vsv...(ii)
On adding Eqs. (i) and (ii), we get
nn+nn′′=2
n=2nnn+n′′

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