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

Given, third harmonic for closed organ pipe

$=$ fundamental frequency for open organ pipe.

$\therefore \quad \frac{3 v}{4 l}=\frac{v}{2 l^{\prime}} \Rightarrow l^{\prime}=\frac{4 l}{3 \times 2}=\frac{2 l}{3}$

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

$l^{\prime}=\frac{2 \times 20}{3}=13.33 \mathrm{cm}$