Question

An organ pipe open at both ends has fundamental frequency $ f $ in air. If the pipe is dipped vertically in water such that $ 1/4^{th} $ of its length is inside water, then the fundamental frequency of the air column in it is

• A. $ f $
• B. $ 2f $
• C. $ \frac{1}{2}f $
• D. $ \frac{2}{3}f $

Answer 1

Answer: (D)

Let $L$ be the length of the pipe. Then its fundamental frequency $f$ is
$f=\frac{v}{2L} \dots(i)$
where $v$ is the speed of sound in air

If the pipe is dipped vertically in water such that $(1/4)^{th}$ of its length is inside the water, then it becomes a closed organ pipe of length $(3/4)L$ as shown in figure above
Now the fundamental frequency of air column is
$f'=\frac{V}{4\left(\frac{3}{4}L\right)}=\frac{v}{3L}$
$\frac{2}{3}\left(\frac{v}{2L}\right)$
$=\frac{2}{3}f $ using (i))