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)

$f$

Answer 2

For cylindrical tube, open at both ends, fundamental frequency is $f = \frac{v}{2L} \quad ...(i)$ where $v$ is the speed of the sound in air and $L$ is the length of the tube. undefined 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 $f' = \frac{v}{4\left(\frac{L}{2} \right)} =\frac{v}{2L} = f$ (Using $(i)$) i.e. the frequency remains unchanged,