Question

A sound source S emitting waves of frequency $100\text{Hz}$ and an observer O are located at some distance from each other. The source is moving with a speed, $V_S=19.4{\text{ms}}^{-1}$ at an angle of ${60}^{\circ }$ with line joining the source and the observe as shown in the figure. If the observer is at rest, the apparent frequency observed by the observer is
(Velocity of sound in air $330{\text{ms}}^{-1})$

• A. $106\text{Hz}$
• B. $97\text{Hz}$
• C. $100\text{Hz}$
• D. $103\text{Hz}$

Answer 1

The correct option is D $103\text{Hz}$

Source frequency $f_0=100\text{Hz}$
Observer is at rest i.e $V_0=0$
Velocity of source , $V_S=19.4\text{m/s}$
Velocity of sound, $v=330\text{m/s}$


Component of velocity of source along line joining the source and the observer is $V_S\cos {60}^{\circ }$
From $f_{app}=f_0\left(\frac{v+0}{v-V_S\cos {60}^{\circ }}\right)$
$\Rightarrow f_{app}=100\left[\frac{330}{330-(19.4\times \frac{1}{2})}\right]$
$\Rightarrow f_{app}=100\left[\frac{330}{320.3}\right]\approx 103\text{Hz}$