Question

An observer moves towards a stationary source of sound, with a velocity one-fifth of the velocity of sound. What is the percentage increase in the apparent frequency?

• A. Zero
• B. $0.5\%$
• C. $5\%$
• D. $20\%$

Answer 1

The correct option is D $20\%$

Let velocity of sound in air be $v$.

$\Rightarrow$ Velocity of observer, $v_{observer}=\frac{v}{5}$

Let $\nu$ be the original frequency of the sound source and ${\nu }^{\prime }$ be the apparent frequency heard by the moving observer.

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

${\nu }^{\prime }=\nu [\frac{v_{sound}+v_{observer}}{v_{sound}}]$ $=\nu [\frac{v+\frac{v}{5}}{v}]=\frac{6}{5}\nu$

Percentage increase in frequency $=\frac{{\nu }^{\prime }-\nu }{\nu }\times 100=\frac{\frac{6}{5}\nu -\nu }{\nu }\times 100=20$ %