Question

A sound is moving towards a stationary listener with $\frac{1}{10}th$ of the speed of 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

Answer: (A)

$\frac{10}{9}$

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 :

$\therefore {\nu }^{\prime }=\nu (\frac{v_{sound}}{v_{sound}-v_{source}})$

$\therefore ,{\nu }^{\prime }=\nu (\frac{v}{v-\frac{v}{10}})⟹\frac{{\nu }^{\prime }}{\nu }=\frac{10}{9}$

Hence, option $\left(A\right)$ is correct.