A stationary source emits sound of frequency $\mathrm{f}_0=492 \mathrm{~Hz}$. The sound is reflected by a large car approaching the source with a speed of $2 \mathrm{~ms}^{-1}$. The reflected signal is received by the soruce and superposed with the original. What will be the beat frequency of the resulting signal in $\mathrm{Hz}$ ? (Given that the speed of sound in air is $330 \mathrm{~ms}^{-1}$ and the car reflects the sound at the frequency it has received).
IIT 2017, Advanced
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Frequencey received by approaching car
$f_1=f_0\left[1+\frac{2}{330}\right]$
Frequency received by source again
$f_2=\frac{f_1}{\left(1-\frac{2}{330}\right)}$
So, beat frequency $f_B=f_2-f_0=6 \mathrm{~Hz}$.
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