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 $330 \; ms^{-1}$ , then the velocity of the observer is

• A. $660\, ms^{-1}$
• B. $330\, ms^{-1}$
• C. $66\, ms^{-1}$
• D. $33\, ms^{-1}$

Answer 1

Answer: (C)

$66\, ms^{-1}$

Answer 2

Given, $n'=\frac{80}{100} \times n$
$v_{S} =0,\, V=330\, ms ^{-1}$
We know that,
$n'=\left(\frac{V-v_{l}}{V-v_{s}}\right) n$
$\Rightarrow \frac{80}{100} \times n=\left(\frac{330-v_{l}}{330-0}\right) n$
$\frac{80}{100}=\frac{330-v_{l}}{330}$
$\Rightarrow \frac{80 \times 330}{100}=330 \cdot v_{l}$
$\Rightarrow 2 v_{l}=330-8 \times 33$
$\Rightarrow v_{l}=330-264$
Velocity of the observer,
$V_{l}=66\, ms ^{-1}$