Question

A source of sound produces waves of wavelength 20 cm in air. It is moving with a velocity one-fourth the velocity of sound towards east. The apparent wavelength noted by a man moving in the same direction with velocity equal to 2/3rd of velocity of sound wave and at the back of source is :

• A. 15 cm
• B. 50 cm
• C. 75 cm
• D. 80 cm

Answer 1

The correct option is A 15 cm

Original wavelength of source ${\lambda }_o=20cm$
Let $f_o$ be the original frequency of the source.
Velocity of source $V_{source}=\frac{V_{sound}}{4}$
Velocity of man $V_{observer}=\frac{2V_{sound}}{3}$
Using Doppler effect when source is moving away from observer while observer is moving towards the source :
Apparent frequency heard by man $f=f_o[\frac{V_{sound}+V_{observer}}{V_{sound}+V_{source}}]$ .......(1)
Using $v=f\lambda$ and $v=f_o{\lambda }_o$ in equation (1), we get
$\frac{1}{\lambda }=\frac{1}{{\lambda }_o}[\frac{V_{sound}+V_{observer}}{V_{sound}+V_{source}}]$
$\therefore$ $\frac{1}{\lambda }=\frac{1}{20}[\frac{V_{sound}+\frac{2V_{sound}}{3}}{V_{sound}+\frac{V_{sound}}{4}}]$
Or $\frac{1}{\lambda }=\frac{1}{20}[\frac{4}{3}]$
$⟹\lambda =15cm$