Question

A cylindrical tube, open at both ends has 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 now

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

Answer 1

Answer: (B)

A cylindrical tube, open at both ends has fundamental frequency $f$
$\therefore f=\frac{\upsilon }{2L}\dots (i)$
where $\upsilon$ is the speed of the sound in air and $L$ is the length of this tube
When this tube is half vertically dipped in water, it becomes a closed pipe of length $L/2$. So, its fundamental frequency becomes
$f^{\prime }=\frac{\upsilon }{4\left(\frac{L}{2}\right)}=\frac{\upsilon }{2L}=f$ (Using (i))