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Question

A boy is walking away from a wall at a speed of 1m/s in a direction at right angle to the wall. As he walks, he blows a whistle steadily. An observer towards whom the boy is walking hears 4 beats per second. If the speed of sound is 340m/s, what is the frequency of the whistle?

A
680 Hz
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B
720 Hz
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C
760 Hz
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D
800 Hz
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Solution

The correct option is A 680 Hz

The situation is equivalent to two sources giving beats. First is the whistle of the boy and the second is wall.
fb=fsfs
4=f(3403401)f(340340+1)
Or 4=f(11340)f(1+1340) on applying binomial approximation,
4=f(1+1340)f(11340)=f170 or f=680 Hz


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