The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is

$\text{ For closed organ pipe, third harmonic is }\frac{3v}{4l}$

$\text{ For open organ pipe, fundamental frequency is }\frac{v}{2l^{\text{'}}}$

Given, third harmonic for closed organ pipe = fundamental frequency for open organ pipe.

$\therefore \frac{3v}{4l}=\frac{v}{2l^{\text{'}}}\Rightarrow l^{\text{'}}=\frac{4l}{3\times 2}=\frac{2l}{3}$

where $l$ and $l^{\mathit{\text{'}}}$ are the lengths of closed and open organ pipes respectively.

$\therefore l\text{'}=\frac{2\times 20}{3}=13.33 \mathrm{cm}$