Question

The frequency of a car horn encountered a change from $400\text{Hz}$ to $500\text{Hz}$, when the car approaches a vertical wall. If the speed of sound is $330\text{m/s}$. Then the speed of car is _____ $\text{km/h}$.

Answer 1

At first, the wall act as the observer.

Frequency received by wall,

$f_1=f_0\left(\frac{v+v_0}{v-v_s}\right)=f_0\left(\frac{v}{v-v^{\prime }}\right)...\left(1\right)$

Now, wall acts as a source.

Frequency received by observer on car,

$f_2=f_1\left(\frac{v+v_0}{v-v_s}\right)=f_1\left(\frac{v+v^{\prime }}{v}\right)...\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$,

$f_2=f_0\left(\frac{v+v^{\prime }}{v-v^{\prime }}\right)$

$\Rightarrow 500=400\left(\frac{330+v^{\prime }}{330-v^{\prime }}\right)$

$\Rightarrow v^{\prime }=\frac{110}{3}\text{m/s}=132\text{km/hr}$