$\nu_{n}^{\prime}=\frac{(2 n-1) v}{4\left(L+0.6 r_{1}\right)} \quad$ where $0.6 r_{1}$ is the end correction

Now for fundamental mode i.e $n=1, \quad \nu_{1}^{\prime}=\frac{v}{4\left(L+0.6 r_{1}\right)}$

For open organ pipe with end correction: Frequency of $m^{t h}$ mode,

$\nu_{m}=\frac{m v}{2\left(L+2 \times 0.6 r_{2}\right)} \quad$ where $0.6 r_{2}$ is the end correction on one side.

Now for first overtonei.e $m=2, \quad \nu_{2}=\frac{2 v}{2\left(L+1.2 r_{2}\right)}$

But $\quad \nu_{1}^{\prime}=\nu_{2}$

$\frac{v}{4\left(L+0.6 r_{1}\right)}=\frac{2 v}{2\left(L+1.2 r_{2}\right)}$

$L+1.2 r_{2}=4 L+2.4 r_{1} \Longrightarrow r_{2}-2 r_{1}=2.5 L$