Q.

Two closed organ pipes A and B have the same length. A is wider than B. They resonate in the fundamental mode at frequencies nA and nB respectively, then

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a

nA=nB

b

nA<nB

c

nA>nB

d

Depending on the ratio of their diameter

answer is C.

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Detailed Solution

In closed organ pipe, first resonance occurs at λ/4. So, in fundamental mode of vibration of organ pipe λ/4=(l+0.3d) where 0.3 d is necessary end correction, then frequency of  vibration,  n=vλ=v4(l+0.3d)

As l is same, wide pipe A will resonate at a lower frequency.

So,  nA<nB.

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