Physics - Sound Wave Question with Solution | TestHub

Let the original length of the air column in the closed organ pipe be $L$.

The fundamental frequency of the closed organ pipe is given by:
$f=\frac{v}{4L}$

When the pipe is filled with water by $\frac{1}{5}$ of its volume, the water occupies a length of $\frac{L}{5}$ at the closed end. The new length of the air column becomes:
$L^{\prime }=L-\frac{L}{5}=\frac{4L}{5}$

The new fundamental frequency is:
$f^{\prime }=\frac{v}{4L^{\prime }}=\frac{v}{4\left(\frac{4L}{5}\right)}=\frac{5}{4}\left(\frac{v}{4L}\right)=\frac{5}{4}f$

The change in frequency is:
$\Delta f=f^{\prime }-f=\frac{5}{4}f-f=\frac{1}{4}f$

The percentage change in the frequency is:
$\frac{\Delta f}{f}\times 100\%=\frac{1}{4}\times 100\%=25\%$

Answer: $25\%$