Question

A source of sound is moving towards a stationary observer with ${\left(\frac{1}{10}\right)}^{th}$ of the speed of sound. The ratio of apparent to real frequency is

[Assume, medium is stationary]

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

Answer 1

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

Let $f_0$ be the frequency of sound heard by the observer, when both the source of sound and observer are at rest.
Let $v$ be the velocity of sound in the stationary medium and $v_s$ be the velocity of the source of sound.

When a source is moving towards a stationary observer, the frequency heard by the observer is given by

$f_{app}=f_0\left(\frac{v}{v-v_s}\right).....\left(1\right)$

From the data given in the question, $v_s=\frac{v}{10}$

Substituting this in the above equation, we get

$f_{app}=f_0\left(\frac{v}{v-\frac{v}{10}}\right)=\frac{10}{9}{f}_0$

$\Rightarrow \frac{f_{app}}{f_0}=\frac{10}{9}$