Question

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

• A. $25 \%$
• B. $20 \%$
• C. $-20 \%$
• D. $-25 \%$

Hint:

The frequency of the fundamental note changes with the length of the pipe.

Answer 1

The Correct Option is A

1. Fundamental frequency: \[ f_1 = \frac{v}{4l} \]
2. Frequency when the tube is filled with water to 4/5 of its length: \[ f_2 = \frac{v}{4(4l/5)} = \frac{5v}{16l} \]
3. Percentage change in frequency: \[ \frac{\Delta f}{f} = \frac{\frac{5v}{16l} - \frac{v}{4l}}{\frac{v}{4l}} \times 100 = 25\% \] Therefore, the correct answer is (1) $25 \%$.