Question

A stationary source (see figure) emits sound waves of frequency $f$ towards a stationary wall. If an observer moving with speed u in a direction perpendicular to the wall measures a frequency $f^{\prime }=\frac{11}{8}f$ at the instant shown, then $u$ is related to the speed of sound $V_S$ as

• A. $\frac{3}{4}Vs$
• B. $\frac{3}{8}Vs$
• C. $\frac{1}{4}Vs$
• D. $\frac{8}{3}Vs$

Answer 1

Answer: (B)

This is the case of Doppler's effect in reflected sound.
The apparent frequency is given by
$f^{\prime }=f\left(\frac{v+v_0}{v-v_s}\right)$
Given, $f^{\prime }=\frac{11}{8}f$
$v_0=u$
$v_s=0$ (stationary source)
$v=v_s$
$\therefore \frac{11}{8}f=f\left(\frac{v_s+u}{v_s}\right)$
$\Rightarrow 11v_s=8\left(v_s+u\right)$
$\Rightarrow u=\frac{3}{8}{v}_s$