In an experiment with a closed organ pipe, it is filled with water by $\left(\frac{1}{5}\right)$ th of its volume. The frequency of the fundamental note will change by

• Correct answer
  A

  $25 \%$
• B

  $20 \%$
• C

  $-20 \%$
• D

  $-25 \%$

Solution

$\lambda_1=4 \ell$
$\mathrm{f}_1=\frac{\mathrm{v}}{4 \ell}$
$\begin{aligned} & \lambda_2=\frac{16 \ell}{5} \\ & \mathrm{f}_2=\frac{5 \mathrm{~V}}{16 \ell} \\ & \frac{\Delta \mathrm{f}}{\mathrm{f}}=\frac{\frac{\mathrm{V}}{\ell}\left(\frac{1}{16}\right)}{\frac{\mathrm{V}}{4 \ell}} \times 100=25 \%\end{aligned}$

Hence, the correct answer is option: 'A'.