Question

A source producing sound of frequency $720 \,Hz$ is falling freely from the top of a tower of height $20\, m$. 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, $g=10 \,ms ^{-2}$ and speed of sound in air $=340 \,ms ^{-1}$ )

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

Answer 1

Answer: (B)

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