A driver in a car, approaching a vertical wall notices that the frequency of his car horn,

Question:

A driver in a car, approaching a vertical wall notices that the frequency of his car horn, has changed from $440 \mathrm{~Hz}$ to $480 \mathrm{~Hz}$, when it gets reflected from the wall. If the speed of sound in air is $345 \mathrm{~m} / \mathrm{s}$, then the speed of the car is :

1. 54 \mathrm{~km} / \mathrm{hr}

2. $36 \mathrm{~km} / \mathrm{hr}$

3. $18 \mathrm{~km} / \mathrm{hr}$

4. $24 \mathrm{~km} / \mathrm{hr}$

Correct Option: 1

Solution:

(1) Let $f_{1}$ be the frequency heard by wall, $f_{1}=\left(\frac{v}{v-v_{c}}\right) f_{0}$

Here, $v=$ Velocity of sound,

$v_{c}=$ Velocity of Car,

$f_{0}=$ actual frequency of car horn

Let $f_{2}$ be the frequency heard by driver after reflection from wall.

$f_{2}=\left(\frac{v+v_{c}}{v}\right) f_{1}=\left(\frac{v+v_{c}}{v-v_{c}}\right) f_{0}$

$\Rightarrow 480=\left[\frac{345+v_{c}}{345-v_{c}}\right] 440 \Rightarrow \frac{12}{11}=\frac{345+v_{c}}{345-v_{c}}$

$\Rightarrow v_{c}=54 \mathrm{~km} / \mathrm{hr}$