Question

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

• A. $33\text{m/s}$
• B. $22\text{m/s}$
• C. Zero
• D. $11\text{m/s}$

Answer 1

The correct option is D $11\text{m/s}$

$n_1=$ Frequency of the police car horn as heard by observer (motorcylist)
$n_2$ = Frequency of the siren heard by the motorcyclist.
$v_2=$Speed of motor cyclist
$n_1=\frac{330-v}{330-22}\times 176;n_2=\frac{330+v}{330}\times 165$
Given that
$\because n_1=n_2\frac{330-v}{330-22}\times 176=\frac{330+v}{330}\times 165\Rightarrow v=11m/s.$