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Question

Question: The frequency of open organ pipe is...

The frequency of open organ pipe is

A

v2l+0.4d\frac{v}{2l+0.4d}

B

v2l+0.6d\frac{v}{2l+0.6d}

C

v2l+0.8d\frac{v}{2l+0.8d}

D

v2l+1.2d\frac{v}{2l+1.2d}

Answer

v2l+0.6d\frac{v}{2l+0.6d}

Explanation

Solution

For an open organ pipe, the effective length is given by:

Leff=l+0.3d(for one end)L_{\text{eff}} = l + 0.3d \quad \text{(for one end)}

Since both ends are open, the total effective length is:

2l+2(0.3d)=2l+0.6d2l + 2(0.3d) = 2l + 0.6d

Thus, the frequency of the fundamental mode is:

f=v2l+0.6df = \frac{v}{2l + 0.6d}