Question

A glass tube of length $1.0m$ is completely filled with water. A vibrating tuning fork of frequency $500Hz$ 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 $330m{s}^{-1},$ then the total number of resonances that occur will be

• A. 2
• B. 3
• C. 1
• D. 5
• E. 4

Answer 1

Answer: (B)

$f=\frac{v}{4l}$ or $l=\frac{v}{4f}$
$\therefore$ $l_1=\frac{v}{4f_1}=\frac{330}{4\times 500}=0.165m;$
$l_2=\frac{3v}{4f_1}=3l_1=0.495;$
$l_3=\frac{5v}{4f_1}=5l_1=0.825m$
And $l_4=\frac{7v}{4f_1}=7l_1=1.155>1m$
Therefore, number of resonance = 3.