Question

A person is riding a motorcycle at a sped $v$ towards a stationary car operating its siren at $165Hz$. A police car is chasing the person at a speed $22m/s$ with its siren operating at $176Hz$. If the motorcyclist does not hear beats, the speed $v\left(m/s\right)$ is (speed of sound in air$=330m/s$)

• A. $33$
• B. $22$
• C. $11$
• D. Zero

Answer 1

The correct option is B $22$

$v_1=176\left[\frac{330-v_0}{330-22}\right]$

$v_2=165\left[\frac{330+v_0}{330}\right]$

But $v_1=v_2$ (as no beats are heard)

$\Rightarrow \frac{176\times (330-v_0)}{308}=\frac{330+v_0}{2}$

$\Rightarrow v_0=22m{s}^{-1}$