The frequency of vibrating air column in a pipe, open at both ends is $f_1$. When…
The frequency of vibrating air column in a pipe, open at both ends is $f_1$. When $\left(\frac{3}{4}\right)^{\text {th }}$ of its length is immersed in water, the frequency of vibrating air column is $f_2$. The value of $\frac{f_1}{f_2}$ is
$\frac{4}{3}$
$\frac{2}{1}$
$\frac{1}{2}$
$\frac{3}{4}$
Solution
Open pipe frequency, $f_1=\frac{v}{2 L}$
Frequency, $f_2=\frac{v}{4(L / 4)}$
( $\because$ when $3 / 4^{\text {th }}$ of length is dipped, it acts as closed pipe of length $\frac{1}{4}$ of length)
So, $\frac{f_1}{f_2}=\frac{v / 2 L}{v / 4(L / 4)}=\frac{1}{2}$