a
For closed organ pipe, third harmonic is \(\frac{3 v}{4 l}\)

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.

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