Question

# A police man on duty detects a drop of 10% in the pitch of the motion of car as it crosses him. If the velocity of sound is 330 m/s. Calculate the speed of the car:

A
17.4 m/s
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B
20.4 m/s
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C
18.6 m/s
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D
16.4 m/s
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Solution

## The correct option is D 16.4 m/sWe know by Doppler effect the f′=f(v±vo)(v±vs)While f′ frequency is the observed f is the original frequency v is the speed of sound vo is the observers speed and vs is the sources speed.i) When the car is approaching the man Then, f1=f(v+o)(v−vs)f′=f(330)(330−v3)ii) When the car is separating from him, Then , f′2=f(v+o)v+vsChange in frequency observed =f′e−f′1 As, pitch drops by 10%△ff=−110⇒△f=−f10So, f′2−f′1=−f10⇒f(v)v+vs−f(v)v−vs=−f10⇒−330[2vs](330)2−vs2=−10⇒v2s−2×3300vs−(330)220By solving, we get vs=−16.458 and vs=6616.45As, second roots is not much practical. Option D is correct as |vs|=16.4 m/s

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