Question

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

• A. $\text{54 km/hr}$
• B. $\text{36 km/hr}$
• C. $\text{18 km/hr}$
• D. $\text{24 km/hr}$

Answer 1

The correct option is A $\text{54 km/hr}$

Let $f_1$ be the frequency recieved at the 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 frequecny heard by driver after reflection from wall.

$f_2=\left(\frac{v+v_c}{v}\right)f_1=\left(\frac{v+v_c}{v-v_c}\right)f_0$
$\Rightarrow 480=\left[\frac{345+v_c}{345-v_c}\right]440\Rightarrow \frac{12}{11}=\frac{345+v_c}{345-v_c}$
$\Rightarrow v_c=15\text{m/s}=54\text{km/hr}$