A source of sound S emitting waves of frequency 100 Hz and an observer O are located at some distance from each other. The source is moving with a speed of 19.4 $m{s}^{-1}$ at an angle of 60° with the source observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer (velocity of sound in air 330 $m{s}^{-1}$), is

 

Here,

$\text{ Frequency of source, }{\nu }_0=100 \mathrm{Hz}$

$\text{ Velocity of source, }{v}_s=19.4{ \mathrm{ms}}^{-1}$

$\text{ Velocity of sound in air, }v=330{ \mathrm{ms}}^{-1}$

As the velocity of source along the source observer line is $v_s$ cos 60° and the observer is at rest, so the apparent frequency observed by the observer is

$\nu ={\nu }_0\left(\frac{v}{v-v_s\cos 60°}\right)$

$=(100 \mathrm{Hz})\left(\frac{330{ \mathrm{ms}}^{-1}}{330{ \mathrm{ms}}^{-1}-\left(19.4{ \mathrm{ms}}^{-1}\right)\left(\frac{1}{2}\right)}\right)$

$=(100 \mathrm{Hz})\left(\frac{330{ \mathrm{ms}}^{-1}}{330{ \mathrm{ms}}^{-1}-9.7{ \mathrm{ms}}^{-1}}\right)$

$=(100 \mathrm{Hz})\left(\frac{330{ \mathrm{ms}}^{-1}}{320.3{ \mathrm{ms}}^{-1}}\right)=103.03 \mathrm{Hz}$