JEE Advanced 2020 Physics question
A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of 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 , the smallest value of the percentage change required in the length of the pipe is .
Answer: 0.62
Solution
For a given mode the resonant length of the pipe is proportional to the wavelength, i.e. . When the fork moves with speed m/s along the line towards (or away from) the open end, the frequency reaching the pipe is Doppler shifted: . Hence
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