Question

A sound source is moving towards stationary listener with $\frac{1}{10}$th of the speed of sound. The ratio of apparent to real frequency is:

• A. ${\left(\frac{9}{10}\right)}^2$
• B. $\frac{10}{9}$
• C. $\frac{11}{10}$
• D. ${\left(\frac{11}{10}\right)}^2$

Answer 1

The correct option is B $\frac{10}{9}$

Let the speed of sound in air be $v$ i.e $v_{sound}=v$

Thus the velocity of source $v_{source}=\frac{v}{10}$

Let $\nu$ and ${\nu }^{\prime }$ be the real frequency of the source and apparent frequency heard by the observer respectively.

Using Doppler effect when the source is moving towards the stationary observer :

$\therefore$ ${\nu }^{\prime }=\nu [\frac{v_{sound}}{v_{sound}-v_{source}}]$

${\nu }^{\prime }=\nu [\frac{v}{v-\frac{v}{10}}]=\frac{10}{9}\nu$ $⟹$ $\frac{{\nu }^{\prime }}{\nu }=\frac{10}{9}$