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  4. An observer is riding on a bicycle and moving towards a hill at 18 kmh -1. He hears a sound from a source at some distance behind him directly as well as after its reflection from the hill. If the original frequency of the sound as emitted by source is 640 Hz and velocity of the sound in air is 320 m / s, the beat frequency between the two sounds heard by observer will be Hz.

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Q. An observer is riding on a bicycle and moving towards a hill at $18 \,kmh ^{-1}$. He hears a sound from a source at some distance behind him directly as well as after its reflection from the hill. If the original frequency of the sound as emitted by source is $640\, Hz$ and velocity of the sound in air is $320\, m / s$, the beat frequency between the two sounds heard by observer will be _______Hz.

JEE MainJEE Main 2022Waves

Solution:

image
$V_S=0, V_{\text {ob }}=5\, m / s$
$ f _{\text {direct }}=\left(\frac{320-5}{320}\right) 640=630\, Hz$
$ f _{\text {reflected }}=\left(\frac{320+5}{320}\right) 640=650\, Hz $
$ f _{\text {beat }}=650-630=20\, Hz $