Question

A source producing sound of frequency $720Hz$ is falling freely from the top of a tower of height $20m$. The frequency of sound heard by an observer on the top of the tower when the source just reaches the ground is (Acceleration due to gravity, $g=10m{s}^{-2}$ and speed of sound in air $=340m{s}^{-1}$ )

• A. 660 Hz
• B. 680 Hz
• C. 740 Hz
• D. 760 Hz

Answer 1

Answer: (B)

$\because$ Final velocity of source, $v_s^2=u_s^2+2gh$
$\Rightarrow v_s=\sqrt{2gh}\left(\because u_s=0\right)$
or $v_s=\sqrt{2\times 10\times 20}=20m/s$
[ Given, $h=20m,g=10m/s^2$]
Frequency of sound heard by an observer,
$n^{{}^{\prime }}=n\left(\frac{v}{v+v_s}\right)$
Given, $n=720Hz,v=340m{s}^{-1}$
$\Rightarrow n^{{}^{\prime }}=720\left(\frac{340}{340+20}\right)=680Hz$