A Closed organ pipe having fundamental frequency f0. Now 1 / 5 of volume its filled with water

Question

A Closed organ pipe having fundamental frequency \(f_0\). Now \(\frac{1}{5}\) of volume its filled with water then \(\%\) change in the fundamental frequency.

(1) \(+10\%\)

(2) \(+25\%\)

(3) \(-20\%\)

(4) \(-10\%\)

Answer 1

Correct option is : (2) \(+25\%\)

\(f _0 = \frac{v}{4L}\)

\(f_0^{'} = \frac{v}{4\left(\frac{4L}{5}\right)} = \frac{5}{4}\left (\frac{v}{4L}\right) = \frac{5}{4}f_0\)

\( = 1.25 \ f_0\)

\(\Rightarrow +25\%\)