A pipe open at both ends has a fundamental frequency f in air. The pipe is dipped vertically in water, so that half of it is in water. The fundamental frequency of the air column is now 

For open ends, fundamental frequency f in air, we have 

$\frac{\lambda }{2}=l\Rightarrow \lambda =2l$
$\mathrm{v}=f\lambda \Rightarrow f=\frac{\mathrm{v}}{\lambda }=\frac{\mathrm{v}}{2l}.....\left(i\right)$
When a pipe is dipped vertically in water, so that half of it is water, we have 

$\frac{\lambda }{4}=\frac{l}{2}$
$\Rightarrow \lambda =2l\Rightarrow \mathrm{v}=f^{\mathrm{\prime }}\lambda \Rightarrow f^{\mathrm{\prime }}=\frac{\mathrm{v}}{\lambda }=\frac{\mathrm{v}}{2l}=f$