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Question

An engine whistling at a constant frequency no and moving with a constant velocity goes past a stationary observer. As the engine crosses him, the frequency of the sound heard by him changes by a factor f(fafter=f×fbefore). The actual difference in the frequencies of the sound heard by him before and after the engine crosses him is :

A
12no(1f2)
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B
12no(1f2f)
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C
no(1f1+f)
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D
12no(1f1+f)
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Solution

The correct option is B 12no(1f2f)
Say n1 is the freq observed by the observer before source cross the observer, and n2 after source crossed the observer. and we are given
that,
n2=fn1, ............................(1)
Also the natural freq of the source is n0.
Then we can write,
n1=VVVsn0
n2=VV+Vsn0
Substitute these values in equation (1),
And apply componendo-dividendo,
We will get, VsV=1f1+f, .....................(2),
We are asked, the difference of
n1n2=⎜ ⎜ ⎜11VsV11+VsV⎟ ⎟ ⎟n0
Substitute the value of VsV from equation (2),
n1n2=12n01f2f,
Option "B" is correct.

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