A source emitting sound of frequency…

A source emitting sound of frequency 680 Hz moves at 10 m s^-1 directly towards a large, stationary plane wall. A stationary observer stands on the…

One or more options correct

A source emitting sound of frequency

680\ \mathrm{Hz}

moves at

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

directly towards a large, stationary plane wall. A stationary observer stands on the line of motion behind the source (so the source moves away from the observer and towards the wall). Take the speed of sound as

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

and no wind. Which of the following statements is/are correct?

A. The frequency of the direct sound heard by the observer is about $660.6\ \mathrm{Hz}$ .
B. The frequency of the sound reflected from the wall and heard by the observer is about $721\ \mathrm{Hz}$ .
C. The observer hears beats of frequency about $40\ \mathrm{Hz}$ .
D. The wavelength of the direct sound reaching the observer is $0.485\ \mathrm{m}$ .

Show answer and solution

Answer: A, C

Direct sound: the source recedes from the observer, so

f_d=f_0\dfrac{v}{v+u}=680\times\dfrac{340}{350}=660.6\ \mathrm{Hz}

: (A) correct. Wavelength of this direct sound is

\lambda_d=\dfrac{v+u}{f_0}=\dfrac{350}{680}=0.515\ \mathrm{m}

, so (D) with

0.485

m (the wavelength in front of the source) is false. The wall, being stationary, receives

f_w=f_0\dfrac{v}{v-u}=680\times\dfrac{340}{330}=700.6\ \mathrm{Hz}

and reflects the same frequency; the stationary observer hears

700.6

Hz, so (B), which states

721

Hz, is false. Beat frequency

=700.6-660.6=40.03\approx40\ \mathrm{Hz}

: (C) correct.

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Original question written in the JEE Advanced 2025 Paper 2 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake