Question

A cylindrical tube open at both ends has a fundamental frequency $f$ in air. The tube is dipped vertically in water so that it has water up to the half height. The fundamental frequency of the air column is now
(Neglect end corrections)

• A. $4f$
• B. $3f$
• C. $f$
• D. $2f$

Answer 1

The correct option is C $f$

For open organ pipe, fundamental frequency,
$f=\frac{v}{2l}$,
where $l$ is the length of an organ pipe.
$\Rightarrow l=\frac{v}{2f}$
After the pipe is half dipped in water, it becomes a closed organ pipe and its new length is,
$l^{{}^{\prime }}=\frac{v}{4f}$
So, fundamental frequency of closed organ pipe,
$f^{{}^{\prime }}=\frac{v}{4l^{{}^{\prime }}}$
[speed is same as medium is same]
$\Rightarrow f^{{}^{\prime }}=\frac{v}{4\times \frac{v}{4f}}=f$