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Question

The speed limit for vehicle on a road is 100 km/hr. A policeman detects a drop of 20% in the pitch of the horn of a car as it passes him. Is the policeman justified in punishing the car driver for crossing the speed limit?
(Velocity of sound =340 m/s).

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Solution

Given
Allowed speed =10kmhr=100×518=27.78ms
Speed of listener VL=0
Velocity of sound in air, v=340ms
Drop in frequency when approaching and receding =20%=0.2
i.e,
na(receding)=na(approaching)20%na(approaching)
=0.8na(approaching)
na=[V±VLVVS]n
Source is approaching listener. Listener is stationary
na(approaching)=[VVVS]n (equation 1)
na(receding)=[VV+VS]n(equation 2)
Dividing equation 2 by 1 we get
na(receding)na(approaching) =[VVSV+VS]
0.8×na(approaching)na(approaching)=[VVSV+VS]
0.8=(VVSV+VS)
0.8V+0.8VS=VVS
0.8VS+VS=V0.8V
1.8VS=0.2V
VS=0.2V1.8=0.2×3401.8=37.77ms
The speed of the car is 37.77ms which is more than the allowed speed of 27.78ms

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