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)

$\frac{2}{3}f$

Answer 2

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))