A closed organ pipe and an open organ pipe of same length produce $2 \mathrm{beats} {\sec }^{-1}$ when they are set into vibrations together in fundamental mode. The length of open pipe is now halved and that of closed pipe is doubled. The number of beats produced will be

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 

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

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

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

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