Question

A police car moving at 22 m/s, chases a motorcyclist. The police man sounds his horn at 176 Hz, while both of them move towards a stationary siren of frequency 165 Hz. Calculate the speed of the motorcycle, if it is given that motor cyclist does not observe any beats.

(velocity of sound in air =330m/s)

• A. 33 m/s
• B. 22 m/s
• C. 55 m/s
• D. 11 m/s

Answer 1

The correct option is B

22 m/s

Motorcyclist listens to two apparent frequencies

(a) police car:
$f_1=f_{01}\left(\frac{330+v}{330-22}\right)=176\left(\frac{330-v}{330}\right)=176\left(\frac{330-v}{308}\right)\left(b\right)siren{f}_2=f_{01}\left(\frac{330+v}{330}\right)=165\left(\frac{330+v}{330}\right)=\left(\frac{330+v}{2}\right)$

Since no beats are present,

$f_1=f_{2}176\left(\frac{330-v}{2}\right)=\frac{330+v}{2}\Rightarrow v=22m{s}^{-1}$