A source emitting a note of frequency…

A source emitting a note of frequency 680 Hz moves at 20 m s^-1 along the line joining a stationary observer O to a large plane reflecting wall…

One or more options correct

A source emitting a note of frequency

680\ \mathrm{Hz}

moves at

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

along the line joining a stationary observer

O

to a large plane reflecting wall, moving directly towards the wall (away from

O

). A steady wind blows at

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

from

O

towards the wall. The speed of sound in still air is

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

. The observer hears the direct sound and the sound reflected from the wall. Which of the following statements is/are correct?

A. The frequency of the direct sound heard by $O$ is about $641\ \mathrm{Hz}$ .
B. The frequency of the reflected sound heard by $O$ is about $721\ \mathrm{Hz}$ .
C. The beat frequency heard by $O$ is about $80\ \mathrm{Hz}$ .
D. The wavelength of the reflected sound in the medium is about $0.50\ \mathrm{m}$ .

Show answer and solution

Answer: A, B, C

Relative to the ground the sound travels towards the wall at

c+w=350\ \mathrm{m\,s^{-1}}

and back towards

O

c-w=330\ \mathrm{m\,s^{-1}}

. Direct sound: the source recedes from

O

, so

f_1=f_0\dfrac{c-w}{(c-w)+v_s}=680\times\dfrac{330}{350}\approx641.1\ \mathrm{Hz}

(A true). The wall (stationary) receives

f=680\times\dfrac{350}{350-20}\approx721.2\ \mathrm{Hz}

and re-radiates this same frequency; since both the wall and

O

are at rest,

O

hears

f_2\approx721.2\ \mathrm{Hz}

(B true). Beats:

f_2-f_1\approx80.1\ \mathrm{Hz}

(C true). The wavelength of the reflected sound is

\lambda=\dfrac{c-w}{f_2}=\dfrac{330}{721.2}\approx0.458\ \mathrm{m}

, not

0.50\ \mathrm{m}

(D false). Correct options: A, B and C.

Original question written in the JEE Advanced 2017 Paper 1 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake