Question

A glass tube $1.0 \,m$ 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 $500\, c/s$ is brought at the upper end of the tube and the velocity of sound is $330\, m/s$ , then the total number of resonances obtained will be

Answer 1

$\lambda = \frac {v}{f} = \frac {330}{500} = 0.66\,m$
The resonance lengths are :
$\ell_{1}=\frac{\lambda}{4}=0.165\,m$ ,
$\ell_{2}=\frac{3\lambda}{4} = 0.495\,m$,
$\ell_{3}=\frac{5\lambda}{4}=0.825\,m$,
and $\ell_{4} = \frac{7\lambda}{4}=1.155\,m$
As $\ell_{4}$ is greater than $1 \,m$, so allowed resonances are only three