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 observes any beats. (velocity of sound in air = 330 m/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

$f_1$ = frequency of the police car heard by motorcyclist,
$f_2$ = frequency of the siren heard by motorcyclist.
$f_1=\frac{330-v}{330-22}\times 176;f_2=\frac{330+v}{330}\times 165;$
$\because f_1-f_2=0\Rightarrow v=22m/s$