Physics - Sound Wave Question with Solution | TestHub

For a pipe open at both ends, the fundamental frequency is given by $f=\frac{v}{2L}$, where $v$ is the speed of sound and $L$ is the length of the pipe.

When the pipe is dipped in water such that $\frac{2}{3}$ of its length is submerged, the length of the air column remaining above the water surface is $L^{\prime }=L-\frac{2L}{3}=\frac{L}{3}$.

The pipe now behaves as a pipe closed at one end. The fundamental frequency of a closed pipe is given by $f^{\prime }=\frac{v}{4L^{\prime }}$.

Substituting $L^{\prime }=\frac{L}{3}$, we get:

$f^{\prime }=\frac{v}{4\left(\frac{L}{3}\right)}=\frac{3v}{4L}$

Since $\frac{v}{2L}=f$, we can write:

$f^{\prime }=\frac{3}{2}\left(\frac{v}{2L}\right)=\frac{3}{2}f$

Answer: $\frac{3}{2}f$