Question

A cylindrical tube open at both the ends has a fundamental frequency of $390Hz$ in air.If $\frac{1}{4}th$ of the tube is immersed vertically in water the fundamental frequency of air column is

• A. $260Hz$
• B. $130Hz$
• C. $390Hz$
• D. $520Hz$

Answer 1

Answer: (A)

$260Hz$

Fundamental frequency of cylindrical open tube
$n=\frac{v}{2L}=390Hz$
When it is immersed in water it becomes a close tube of length $\frac{3}{4}th$ of the initial length.
Therefore ,its fundamental frequency is
$n=\frac{v}{4\left(\frac{3}{4}L\right)}=\frac{v}{3L}=\frac{2}{3}\left(\frac{v}{2L}\right)$
$=\frac{2}{3}\times 390Hz=260Hz$