Question

A glass tube $1.0m$ length is filled with water. The water can be drained out slowly at the bottom of the tube. If a vibrating tunning fork of frequency $500c/s$ is brought at the upper end of the tube and the velocity of sound is $330m/s$ , then the total number of resonances obtained will be

Answer 1

Answer: 3

$\lambda =\frac{v}{f}=\frac{330}{500}=0.66m$
The resonance lengths are :
${\ell }_1=\frac{\lambda }{4}=0.165m$ ,
${\ell }_2=\frac{3\lambda }{4}=0.495m$,
${\ell }_3=\frac{5\lambda }{4}=0.825m$,
and ${\ell }_4=\frac{7\lambda }{4}=1.155m$
As ${\ell }_4$ is greater than $1m$, so allowed resonances are only three