A source of sound $S$ emitting waves of frequency $100\,\, Hz$ and an observer $O$ are ocated at some distance from each other. The source is moving with a speed of $19 .4\,\, m s^{-1}$ at an angle of $60^o $ with the source observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer .... $Hz$ (velocity of sound in air $330 \,\, m s^{-1}$), is
AIPMT 2015, Diffcult
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Here,
Frequency of source, $v_{0}=100 \mathrm{Hz}$
Velocity of source, $v_{s}=19.4 \mathrm{ms}^{-1}$
Velocity of sound in air, $v=330 \mathrm{ms}^{-1}$
As the velocity of source along the source observer line is $v_{s} \cos 60^{\circ}$ and the observer is at rest, so the apparent frequency observed by the observer is
${v=v_{0}\left(\frac{v}{v-v_{s} \cos 60^{\circ}}\right)}$
${=(100 \mathrm{Hz})\left(\frac{330 \mathrm{ms}^{-1}}{330 \mathrm{ms}^{-1}-\left(19.4 \mathrm{ms}^{-1}\right)\left(\frac{1}{2}\right)}\right)}$
${=(100 \mathrm{Hz})\left(\frac{330 \mathrm{ms}^{-1}}{330 \mathrm{ms}^{-1}-9.7 \mathrm{ms}^{-1}}\right)}$
${=(100 \mathrm{Hz})\left(\frac{330 \mathrm{ms}^{-1}}{320.3 \mathrm{ms}^{-1}}\right)=103 \mathrm{Hz}}$
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