Physics - Sound Wave Question with Solution | TestHub

Velocity of bike $V_b=30 {\text{m s}}^{\text{-1}}$
Let the velocity of car be $V_c$

$f_{obs} = f_{actual}\times \frac{V_{so}+V_b}{V_{so}-V_c}$
$120 \text{Hz }=100 \text{Hz}\times \frac{330+30}{330-V_c}$
$\Rightarrow V_c=30 {\text{m s}}^{\text{-1}}$

Distance between initial and final pulse of horn
$=V_{so}\times \Delta t-V_c\Delta t$                  ( $\Delta t$ is duration of emission of sound)
$=\left(330-30\right)\times 6=1800\text{m}$

This wave train travels with $330{\text{m s}}^{\text{-1}}$ and cross bike rider moving with velocity of $30{\text{m s}}^{\text{-1}}$ towards it.

Time taken $=\frac{\text{length of wave train}}{V_{so}+V_b}=\frac{1800}{330+30}=\frac{180}{36}=5\text{ s}$