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A policeman on duty detects a drop dete...

A policeman on duty detects a drop detects a drop of `15%` in the pitch of the horn of a motor car as it crossed him. If the velocity of sound is `330metre //sec`., calculate speed of the car.

Text Solution

Verified by Experts

The correct Answer is:
17.37 m/s
While car is approching apparent frequency is
`n_(ap1) = n_(0) ((v)/(v - v_(c)))`
while recording away apparent frequency is
`n_(ap2) = n_(0) ((v)/(v + v_(c)))`
Given that percentage drop in pitch is 10% Thus we use
`(n_(ap1) - n_(ap2))/(n_(ap1)) xx100 = 0`
`((v)/(v - v_(c)) - (v)/(v+v_(c)))/((v)/(v -v_c)) = 0.1`
`10((2v_(c))/(v+v_(c))) = 1`
`20v_(c) = v + v_(c)`
`v_(c) = (v)/(19) = (330)/(19)` = 17.37 m/s
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