Question

A sound is moving towards stationery with ${\frac{1}{10}}^{th}$ of the sound. The ratio of apparent to real frequency is

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

Answer 1

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

Let the speed of sound in the air be $v$ that is $v_{sound}=v$

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 the Doppler effect when the source is moving towards the stationary observer;

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

${\nu }^{\prime }=\nu \left[\frac{\nu }{\nu -\frac{\nu }{10}}\right]=\frac{10}{9}\nu$

$\Rightarrow \frac{{\nu }^{\prime }}{\nu }=\frac{10}{9}$