Question

A source of sound of frequency n and a listener approach each other with a velocity equal to $ \frac{1}{20} $ of velocity of sound. The apparent frequency heard by the listener is

• A. $ \left( \frac{21}{19} \right)n $
• B. $ \left( \frac{20}{21} \right)n $
• C. $ \left( \frac{21}{20} \right)n $
• D. $ \left( \frac{19}{20} \right)n $

Answer 1

Answer: (A)

From Doppler's effect, the perceived frequency $\left(n^{\prime}\right)$ is given by
$n'=\left(\frac{v+v_{o}}{v-v_{s}}\right) n$
where $:$ ' is velocity of sound, $v_{o}$ of observer and $v_{s}$ of source.
Given, $ v_{o}=\frac{v}{20}, v_{s}=\frac{v}{20}$
$ n'=\left(\frac{v+\frac{v}{20}}{v-\frac{v}{20}}\right) n $
$ \therefore n'=n\left(\frac{21 v}{19 v}\right)=\left(\frac{21}{19}\right) n$