Two closed organ pipe A and B have the same length. A is wider than B. They resonate in the fundamental mode at frequencies `V_(A) and V_(B)` respectively , then

Options

A. `n_(A) = n_(B)`
B. `n_(A) gt n_(B)`
C. `n_(A) lt n_(B)`
D. Either (b) or ( c) depending on the ratio of their diameters

Answer

c

Explanation

In closed organ pipe. First resonance occurs at `lambda//4.`
So, in fundamental mode of vibration of organ pipe
`lambda/4=(l+0.3d)`
where, `0.3` d is necessary end correction.
Frequency of vibration, `n=v/lambda = v/(4(l+0.3d))`
As / is same, wide pipe A will resonate at a lower
Frequency, I.e. `n_(A) lt n_(B).`