A closed organ pipe and an open organ pipe of same length produce 2   beats   sec - 1 when they…

Fundamental frequency of closed organ pipe $f_c=\frac{v}{4l}$ 

Fundamental frequency of open organ pipe $f_o=\frac{v}{2l}$

Initial beats frequency 

$f_o-f_c=2$

$\Rightarrow \frac{v}{2l}-\frac{v}{4l}=2$

$\Rightarrow \frac{v}{4l}=2$

$\Rightarrow \frac{v}{l}=8$

After changing of length 

 Fundamental frequency of closed organ pipe $f_c^{\text{'}}=\frac{v}{4\left({\displaystyle 2l}\right)}=\frac{v}{8l}$

Fundamental frequency of open organ pipe $f_o^{\text{'}}=\frac{v}{2\left({\displaystyle \frac{{\displaystyle l}}{2}}\right)}=\frac{v}{l}$

New beats frequency 

$f_o^{\text{'}}-f_c^{\text{'}}$

$=\frac{v}{l}-\frac{v}{8l}$

$=\frac{7v}{8l}$

$=\frac{7\times 8}{8}=7$