JEE Advanced 2023 Paper 1 · Physics · Waves and Sound · medium

A source emits a steady note of frequency 600 Hz while moving at 30 m s^-1 directly towards a large plane wall. A stationary observer stands on the…

Numerical answer

A source emits a steady note of frequency

600\ \mathrm{Hz}

while moving at

30\ \mathrm{m\,s^{-1}}

directly towards a large plane wall. A stationary observer stands on the line joining the source and the wall, behind the source (so the source is between the observer and the wall). The speed of sound is

330\ \mathrm{m\,s^{-1}}

and there is no wind. The number of beats per second heard by the observer, between the direct sound and the sound reflected from the wall, is

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Answer: 110

The observer is behind the receding source, so the direct sound is lowered:

f_1=f\dfrac{v}{v+u}=600\times\dfrac{330}{360}=550\ \mathrm{Hz}

. The wall is a stationary receiver towards which the source approaches, so it receives

f_2=f\dfrac{v}{v-u}=600\times\dfrac{330}{300}=660\ \mathrm{Hz}

. A stationary wall reflects the sound at the same frequency, and the stationary observer, who is at rest relative to the medium and the wall, hears this reflected sound at

660\ \mathrm{Hz}

. The beat frequency is

660-550=110\ \mathrm{Hz}

. In closed form

f_b=\dfrac{2fvu}{v^2-u^2}=\dfrac{2\times600\times330\times30}{330^2-30^2}=110\ \mathrm{Hz}

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