Question

A car is moving towards a huge wall with a speed $\frac{c}{10}$, where c = speed of sound in still air. A wind is also blowing parallel to the velocity of the car in the same direction and with the same speed. If the car sounds a horn of frequency $f$, then the frequency of the reflected sound of the horn heared by driver of the car is $\frac{xf}{9}$. Find the value of $x$ :

Answer 1

In the wind frame, the wall appears to move towards the car with a speed of $\frac{c}{10}m/s$ and car is at rest w.r t wind.

Let $f^{\prime \prime }$ be the frequency of the reflected sound of horn heard by the driver.

Given: Frequency of the horn $=f$

Doppler effect when wall act as an observer and car as source:

$f^{\prime }=f[\frac{v_{sound}+v_{wall}}{v_{sound}}]$

$f^{\prime }=f[\frac{c+\frac{c}{10}}{c}]=\frac{11}{10}f$

Doppler effect when car act as an observer and wall as source:

$f^{\prime \prime }=f^{\prime }[\frac{v_{sound}}{v_{sound}-v_{wall}}]$

$f^{\prime }=\frac{11}{10}f\times [\frac{c}{c-\frac{c}{10}}]=\frac{11}{9}f$

$⟹x=11$