Question

The apparent frequency observed by a moving observer away from a stationary source is $20$% less than the actual frequency. If the velocity of sound in air is $330m{s}^{-1}$, then the velocity of the observer is

• A. $660m{s}^{-1}$
• B. $330m{s}^{-1}$
• C. $66m{s}^{-1}$
• D. $33m{s}^{-1}$
• E. $20m{s}^{-1}$

Answer 1

Answer: (C)

$66m{s}^{-1}$

Given, $n^{\prime }=\frac{80}{100}\times n$,
$v_s=0,v=330m{s}^{-1}$
We know that,
$n^{\prime }=\left(\frac{v-v_1}{v-v_s}\right)n$
$\Rightarrow \frac{80}{100}\times n=\left(\frac{330-v_1}{330-0}\right)n$
$=\frac{80}{100}=\frac{330-v_1}{330}$
$\Rightarrow \frac{80\times 330}{100}=330-v_l$
$\Rightarrow v_l=330-8\times 33$
$\Rightarrow v_l=330-264$
Velocity of the observer,
$v_l=66m{s}^{-1}$.