JEE Main 2021 · Physics · Waves and Sound · medium

A source of frequency 1440 Hz moves at 20 m s^-1 directly towards a large flat wall. A stationary observer stands on the line of motion behind the…

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A source of frequency

1440\ \mathrm{Hz}

moves at

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

directly towards a large flat wall. A stationary observer stands on the line of motion behind the source (so the source moves away from the observer). Speed of sound is

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

. The beat frequency heard by the observer between the direct sound and the sound reflected from the wall is

A. $85\ \mathrm{Hz}$
B. $170\ \mathrm{Hz}$
C. $180\ \mathrm{Hz}$
D. $340\ \mathrm{Hz}$

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Answer: (B) $170\ \mathrm{Hz}$

Direct sound (source receding):

f_1=\dfrac{fv}{v+v_s}=\dfrac{1440\times340}{360}=1360\ \mathrm{Hz}

. The wall receives and re-emits the sound from the approaching source:

f_2=\dfrac{fv}{v-v_s}=\dfrac{1440\times340}{320}=1530\ \mathrm{Hz}

. Beats

=f_2-f_1=170\ \mathrm{Hz}

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