In an organ pipe closed at one end produces a fundamental note of frequency ' ν '. The pipe is cut into two pipes of equal length. The fundamental frequencies produced in the two pipes are

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Let the length of the original closed organ pipe be $L$ .

The fundamental frequency of the closed organ pipe is given by $ν = \frac{v}{4 L}$ .

When the pipe is cut into two equal halves, the length of each half becomes $L^{'} = \frac{L}{2}$ .

One of the halves will be a closed organ pipe (having the original closed end) and the other half will be an open organ pipe (having both ends open).

For the closed half, the fundamental frequency is $ν_{1} = \frac{v}{4 L ^{'}} = \frac{v}{4 ( L /2 )} = \frac{v}{2 L} = 2 (\frac{v}{4 L}) = 2 ν$ .

For the open half, the fundamental frequency is $ν_{2} = \frac{v}{2 L ^{'}} = \frac{v}{2 ( L /2 )} = \frac{v}{L} = 4 (\frac{v}{4 L}) = 4 ν$ .

Thus, the fundamental frequencies produced in the two pipes are $2 ν$ and $4 ν$ .

Answer: $2 ν$ , $4 ν$

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