JEE Main · 2016 · 03 Apr 2016 · Offline · Waves & Sound

Open at both ends and of length $\ell$, the pipe sounds its fundamental at $f=\frac{v}{2\ell }$. Dipping it so that half is under water seals the lower end at the water surface, turning it into a pipe closed at one end with air column $\frac{\ell }{2}$. A closed pipe has fundamental $\frac{v}{4{\ell }^{\prime }}$, and here ${\ell }^{\prime }=\frac{\ell }{2}$, so $f^{\prime }=\frac{v}{4(\ell /2)}=\frac{v}{2\ell }=f$. The fundamental frequency stays the same.