Question

A policeman on duty detects a drop of $10$% in the frequency of the horn of a motor car as it crosses him. If the velocity of sound is $330m/s$, the speed of the car is :

• A. $20m/s$
• B. $36.67m/s$
• C. $25m/s$
• D. none of the above

Answer 1

The correct option is D none of the above

Let the actual frequency of the horn be $f_o$.

Thus apparent frequency heard by policeman $f=0.9f_o$

Velocity of sound in air $v=330m/s$

Let the velocity of car be $v_{car}$.

Using Doppler effect when the source (car) moves away from stationary observer (policeman) :

$f=f_o[\frac{v}{v+v_{car}}]$

Or $0.9f_o=f_o[\frac{330}{330+v_{car}}]$

Or $330+v_{car}=366.67$

$⟹v_{car}=36.67m/s$