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' = \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
$f '= f \left(\frac{ v + v _{0}}{ v - v _{ s }}\right)$
Given, $f '=\frac{11}{8} f$
$v _{0} = u$
$v_{ s }=0$ (stationary source)
$v = v _{ s }$
$\therefore \frac{11}{8} f = f \left(\frac{ v _{ s }+ u }{ v _{ s }}\right)$
$\Rightarrow 11 v _{ s }=8\left( v _{ s }+ u \right)$
$\Rightarrow u =\frac{3}{8} v _{ s }$