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Q.

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 ms−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 ms−1, the smallest value of the percentage change required in the length of the pipe is _________

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answer is 0.62.

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Detailed Solution

f∝1ℓ1⇒f=kℓ1 …....(1)ℓ1⇒ initial length of pipe VV−VTf=kℓ2VT Speed of tuning fork ℓ2→ newlength of pipe  ……(2)(1)÷(2)V−VTV=ℓ2ℓ1ℓ2ℓ1−1=V−VTV−1ℓ2−ℓ1ℓ1=−VTVℓ2−ℓ1ℓ1×100=−2320×100=−0.625Therefore smallest value of percentage change required in the length of pipe is 0.625
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