Question

A glass tube of length $1.0\, m$ is completely filled with water. A vibrating tuning fork of frequency $500 \,Hz$ is kept over the mouth of the tube and the water is drained out slowly at the bottom of the tube. If velocity of sound in air is $330\,m{{s}^{-1}},$ then the total number of resonances that occur will be

• A. 2
• B. 3
• C. 1
• D. 5

Answer 1

Answer: (B)

3

Answer 2

$f=\frac{v}{4l}$ or $l=\frac{v}{4f}$
$\therefore$ ${{l}_{1}}=\frac{v}{4{{f}_{1}}}=\frac{330}{4\times 500}=0.165\,m;$
${{l}_{2}}=\frac{3v}{4{{f}_{1}}}=3{{l}_{1}}=0.495;$
${{l}_{3}}=\frac{5v}{4{{f}_{1}}}=5{{l}_{1}}=0.825\,m$
And ${{l}_{4}}=\frac{7v}{4{{f}_{1}}}=7{{l}_{1}}=1.155>1\,m$
Therefore, number of resonance = 3.