Question

A cylindrical tube, open at both ends, has a fundamental frequency $f$ in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is

• A. $2f$
• B. $\frac{3}{4}f$
• C. $\frac{f}{2}$
• D. $f$

Answer 1

Answer: (D)

For cylindrical tube, open at both ends, fundamental frequency is
$f=\frac{v}{2L}...(i)$
where $v$ is the speed of the sound in air and $L$ is the length of the tube.

When half of its length dipped vertically in water, then it will become a closed tube with half the length of the air column, so its fundamental frequency is

$f^{\prime }=\frac{v}{4\left(\frac{L}{2}\right)}=\frac{v}{2L}=f$ (Using $(i)$)
i.e. the frequency remains unchanged,