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PhysicsNumerical+4Question 17 of 54

JEE Advanced 2020 · Paper 1, Physics question 17

A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of 2 m s−12\ \mathrm{m\,s^{-1}} in front of the open end of the pipe and parallel to it, the length of the pipe should be changed for the resonance to occur with the moving tuning fork. If the speed of sound in air is 320 m s−1320\ \mathrm{m\,s^{-1}}, the smallest value of the percentage change required in the length of the pipe is ______.

Answer and worked solution

Official answer: 0.62

The pipe resonates at a fixed mode, so its resonant length is inversely proportional to the frequency it receives: L∝1/f′L\propto1/f'.

Doppler shift of a source moving at vs=2 m s−1v_s=2\ \mathrm{m\,s^{-1}} along the pipe's axis:

  • approaching: f′=f320318f'=f\dfrac{320}{318}, so LL must shrink by 2320=0.625%\dfrac{2}{320}=0.625\%;
  • receding: f′=f320322f'=f\dfrac{320}{322}, so LL must grow by 2322=0.621%\dfrac{2}{322}=0.621\%.

The smaller change is about 0.62%0.62\%.

Answer: 0.62 (key: 0.62 to 0.64)

Topics:Doppler effectOrgan pipes and resonance
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