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 he does not observe any beats.

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

Answer 1

The correct option is B

22 m/s

$n_1$ = Frequency of the police car horn heard by motorcyclist

$n_2$ = Frequency of the siren heard by motorcyclist.

$v$ = Speed of motor cyclist

$n_1$ = $\frac{330-v}{330-22}\times 176$; $n_2$ = $\frac{330+v}{330}\times 165$

$\because$ $n_1$ - $n_2$ = 0 $\Rightarrow$ $v$ = $22m{s}^{-1}$.