A stationary source emits sound of…

A stationary source emits sound of frequency 680 Hz towards a large flat wall that moves towards the source at 10 m s^-1. The speed of sound in still…

One or more options correct

A stationary source emits sound of frequency

680\ \mathrm{Hz}

towards a large flat wall that moves towards the source at

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

. The speed of sound in still air is

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

. Choose the correct statement(s).

A. In still air the frequency of the sound incident on the wall is $700\ \mathrm{Hz}$ .
B. In still air the wavelength of the reflected sound is $0.50\ \mathrm{m}$ .
C. In still air the source hears the reflected sound beating with its own sound at $40\ \mathrm{Hz}$ .
D. If a steady wind of $20\ \mathrm{m\,s^{-1}}$ blows from the source towards the wall, the beat frequency heard at the source exceeds $45\ \mathrm{Hz}$ .

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Answer: A

The wall is a moving observer:

f_w=f(c+u)/c=680\times350/340=700\ \mathrm{Hz}

, so A is true. It then acts as a moving source of frequency

f_w

, so the reflected wavelength is

\lambda'=(c-u)/f_w=330/700=0.471\ \mathrm{m}

, not

0.50\ \mathrm{m}

; B is false. The reflected frequency heard by the stationary source is

f_r=f(c+u)/(c-u)=680\times350/330=721.2\ \mathrm{Hz}

, so the beat frequency is

41.2\ \mathrm{Hz}

, not

40\ \mathrm{Hz}

; C is false. With wind speed

w

along the source-to-wall direction,

f_r=f\dfrac{(c+w+u)(c-w)}{(c+w)(c-w-u)}=721.4\ \mathrm{Hz}

, so the beat frequency is about

41.4\ \mathrm{Hz}

, which is below

45\ \mathrm{Hz}

; D is false.

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Original question written in the JEE Advanced 2016 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