Question

A wall is moving with constant velocity $u$ towards a fixed source of sound of frequency $f$. The velocity of sound is $v$. Then the wavelength of the sound reflected by the wall is

• A. $\frac{v}{f}$
• B. $\frac{v-u}{f}$
• C. $\frac{v+u}{f}$
• D. $\frac{v-u}{v+u}.\frac{v}{f}$

Answer 1

The correct option is D $\frac{v-u}{v+u}.\frac{v}{f}$

Given, velocity of sound = $v$
velocity of wall = $u$
then, relative speed of sound w.r.t. wall before reflection= $v+u$
Let, apparent frequency of the wall is $f^{\prime }$.
Then, $f^{\prime }=\left(\frac{v+u}{v}\right)f$ .......(1)
Relative speed of sound w.r.t. wall after reflection = $v-u$
$\therefore$ wavelength of sound reflected by wall $=\frac{v-u}{f^{\prime }}$
Putting $f^{\prime }$ value from equation (1)
Wavelength of sound reflected by wall $=\frac{v-u}{v+u}\times \frac{v}{f}$
Hence, option (4) matches correctly.