JEE Main 2025 · Physics · Waves and Sound · medium

A source of frequency 300 Hz moves at 30 m s^-1 directly towards a large flat wall. A stationary observer stands on the line of motion on the far…

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A source of frequency

300\ \mathrm{Hz}

moves at

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

directly towards a large flat wall. A stationary observer stands on the line of motion on the far side of the source from the wall, so that he hears both the direct sound and the sound reflected by the wall. Taking the speed of sound as

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

, the beat frequency heard by him is

A. $25\ \mathrm{Hz}$
B. $30\ \mathrm{Hz}$
C. $55\ \mathrm{Hz}$
D. $60\ \mathrm{Hz}$

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Answer: (C) $55\ \mathrm{Hz}$

The observer sees the source receding, so the direct sound has

f_1 = f\,\dfrac{v}{v+v_s} = 300\cdot\dfrac{330}{360} = 275\ \mathrm{Hz}

. The wall is a stationary receiver of a source approaching it, so it receives and re-radiates

f_2 = f\,\dfrac{v}{v-v_s} = 300\cdot\dfrac{330}{300} = 330\ \mathrm{Hz}

. The stationary observer hears this reflected sound at

330\ \mathrm{Hz}

. Beat frequency

= 330 - 275 = 55\ \mathrm{Hz}

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