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JEE Advanced 2024 Paper 1 · Physics · Waves and Sound · medium

A source emitting a pure tone of frequency 720 Hz moves with speed 20 m s^-1 along a straight line towards a large flat wall that is perpendicular to…

One or more options correct

A source emitting a pure tone of frequency 720 Hz720\ \mathrm{Hz} moves with speed 20 m s−120\ \mathrm{m\,s^{-1}} along a straight line towards a large flat wall that is perpendicular to its path. A stationary observer stands on the same line behind the source, so the source moves away from the observer. Speed of sound in air is 340 m s−1340\ \mathrm{m\,s^{-1}} and there is no wind. Which of the following statements is/are correct?
  1. A. The frequency of the sound reaching the observer directly from the source is 680 Hz680\ \mathrm{Hz}.
  2. B. The frequency of the sound reaching the observer after reflection from the wall is 765 Hz765\ \mathrm{Hz}.
  3. C. The observer hears beats at a frequency of 80 Hz80\ \mathrm{Hz}.
  4. D. The wavelength of the sound waves travelling in air from the source towards the wall is about 0.444 m0.444\ \mathrm{m}.
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Answer: A, B, D

Direct sound: the source recedes from the observer, so fd=f0vv+vs=720⋅340360=680 Hzf_d=f_0\dfrac{v}{v+v_s}=720\cdot\dfrac{340}{360}=680\ \mathrm{Hz}. Option A is correct. Sound travelling towards the wall is emitted by an approaching source: wavelength λ=v−vsf0=320720=0.444 m\lambda=\dfrac{v-v_s}{f_0}=\dfrac{320}{720}=0.444\ \mathrm{m}, so the frequency received by the wall is fw=v/λ=765 Hzf_w=v/\lambda=765\ \mathrm{Hz}. D is correct. A stationary wall re-emits this same frequency and the observer is stationary, so the reflected sound is heard at 765 Hz765\ \mathrm{Hz} (B correct). Beat frequency =765−680=85 Hz=765-680=85\ \mathrm{Hz}, not 80 Hz80\ \mathrm{Hz}, so C is wrong. The key idea is that the wall, being stationary, re-radiates exactly the frequency it receives, so the only Doppler shifts are those caused by the moving source in each of the two paths.
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Original question written in the JEE Advanced 2024 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