Question

In the figure shown, a source of sound at A having frequency $510\text{Hz}$ moves with constant velocity $v_s=20\text{m/s}$ in the direction shown. The wind is blowing at a constant velocity $v_w=20\text{m/s}$ towards an observer who is at rest at point $B$. Frequency detected by the observer corresponding to the sound emitted by the source at initial position $A$ will be
$($speed of sound relative to air $=330\text{m/s})$

• A. $485\text{Hz}$
• B. $500\text{Hz}$
• C. $512\text{Hz}$
• D. $525\text{Hz}$

Answer 1

The correct option is D $525\text{Hz}$

Given:
Frequency of the sound, $f_o=510\text{Hz}$
Speed of source of sound, $v_s=20\text{m/s}$
Speed of wind, $v_w=20\text{m/s}$
Speed of sound, $v=330\text{m/s}$
So, apparent frequency heard by the observer,
$f=\left(\frac{v+v_w+v_o}{v+v_w-v_s^{{}^{\prime }}}\right)\times f_o$
$\Rightarrow f=\left(\frac{330+20+0}{330+20-20\sin {30}^{\circ }}\right)\times 510$
$\Rightarrow f=525\text{Hz}$

Caution: Always take the velocities of observer, source and wind along the line joining the source and observer.