In an experiment with a closed organ pipe, it is filled with water by $\left(\frac{1}{5}\right)$ th of its…

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
  1. $25 \%$
  2. $20 \%$
  3. $-20 \%$
  4. $-25 \%$

Solution


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

Asked in: JEE Main 2025 (04 Apr Shift 1)

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