Question

A glass tube of $1.0m$ length is filled with water. The water can be drained out slowly at bottom of the tube. If a vibrating turning fork of frequency $500Hz$ is brought at the upper end of the tube and the velocity of sound is $330m{s}^{-1}$, then the total number of resonances obtained will be:

• A. 4
• B. 3
• C. 2
• D. 1

Answer 1

The correct option is B 3

Wavelength of the sound produced is,
$\lambda =\frac{Velocity}{Frequency}$

$=\frac{330m{s}^{-1}}{500s^{-1}}=0.66m$

The resonance occurs at
$\frac{\lambda }{4},\frac{3\lambda }{4},\frac{5\lambda }{4},\frac{7\lambda }{4},.....$

i.e., at $0.165m,0.495m,0.825m,1.155m$. As the length of the tube is only $1.0m$, hence $3$ resonance will be observed.