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

## GivenAllowed speed =10kmhr=100×518=27.78msSpeed of listener VL=0Velocity of sound in air, v=340msDrop in frequency when approaching and receding =20%=0.2i.e,na(receding)=na(approaching)−20%na(approaching)=0.8na(approaching)na=[V±VLV∓VS]nSource is approaching listener. Listener is stationary∴na(approaching)=[VV−VS]n (equation 1) ∴na(receding)=[VV+VS]n(equation 2)Dividing equation 2 by 1 we get ∴na(receding)na(approaching) =[V−VSV+VS]∴0.8×na(approaching)na(approaching)=[V−VSV+VS]∴0.8=(V−VSV+VS)∴0.8V+0.8VS=V−VS⇒0.8VS+VS=V−0.8V⇒1.8VS=0.2V⇒VS=0.2V1.8=0.2×3401.8=37.77msThe speed of the car is 37.77ms which is more than the allowed speed of 27.78ms

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