Question

A policeman on duty detects a drop of $10\%$ in the pitch of the horn of a moving car as it crosses him. If the velocity of sound is $330m/s$, the speed of the car will be

• A. $36.7m/sec$
• B. $17.3m/sec$
• C. $25m/sec$
• D. $27m/sec$

Answer 1

The correct option is A $36.7m/sec$

Drop of $10\%$

$\Rightarrow$ Hears frequency was $90\%$ of original so if original$=v$

Then apparent$=0.9$v

Using

$v^{\prime }=v\left(\frac{v}{v+vs}\right)$; vs$=$ speed of car

Put $v^{\prime }=0.9v$

We get

$0.9=\frac{v}{v+vs}$

$\Rightarrow 0.9v+0.9vs=v$

or $0.9vs=0.1v$

$\Rightarrow vs=\frac{v}{9}$

Put $v=330$m/s

$vs=\frac{330}{9}=36.7$m/s.