A tube open at both the ends has a fundamental frequency $f$ in air. If the half tube is dipped vertically…
A tube open at both the ends has a fundamental frequency $f$ in air. If the half tube is dipped vertically in water, then the fundamental frequency of the air column is [Kerala CEE 2013]
$\frac{f}{2}$
$\frac{3f}{2}$
$\frac{3f}{4}$
$f$
$2f$
Solution
In given case, pipe will behave as closed pipe. We know the frequency for a open pipe is $f = \frac{v}{2l}$
But frequency after filling with water, $f' = \frac{v}{4l'}$
Here, $l' = \frac{l}{2}$, so that $f' = \frac{v}{4l/2}$
$f' = \frac{2v}{4l} = \frac{v}{2l}$, $f' = f$