Question

A car is moving towards a huge wall with a sspeed 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 9xf​. Find the value of x :

Answer 1

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Answer 2

Answer:

x = 11/81

Explanation:

Formula to be used for Doppler's effect :  $f' = \frac{v + v_{o} }{v - v_{s} }$$f$

where f' is the frequency after modification.

v is the velocity of sound wave

$v_{o}$ is the velocity of observer

$v_{s}$ is the velocity of source

and, f is the actual frequency.

Solving everything with respect to car. So, the velocity of source initially will be zero. Velocity of observer (wall) will be c/10 towards car.

First case is when the sound of horn reaches the wall:

f' = $\frac{c + \frac{c}{10} }{c - 0}$$f$

because, the source's (car's) speed is c/10.

and the observer's (wall) speed is 0.

f' = $\frac{10c +c}{10c}$$f$

f' = $\frac{11}{10} f$

In the second case also with respect to car, velocity of source (wall) is c/10 towards car. Velocity of observer (car) is zero.

Second case is when the sound of horn is reflected by the wall:

f' = $\frac{c + 0}{c - \frac{c}{10} } (\frac{11f}{10} )$

f' = $\frac{10c}{9c} X \frac{11f}{10}$

f' = $\frac{11f}{9}$

Given - f' = 9xf

so, 9xf = 11f/9

x = 11/81.

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