Question

A glass tube of 2 m length is filled with water. The water can be drained out slowly at the bottom of the tube. If a vibrating tuning fork of frequency 500 Hz is brought at the upper end of the tube and the velocity of sound is 300 m/s, then the total number of resonances obtained will be

• A. 6
• B. 7
• C. 2
• D. 0

Answer 1

The correct option is B 7

Velocity, $v=f\lambda$
$\Rightarrow \lambda =\frac{v}{f}=\frac{300}{500}=0.6m$
$\therefore$ Resonance will occur for $l\ge (2n+1)\frac{\lambda }{4}$
$\Rightarrow 2\ge (2n+1)\frac{0.6}{4}$
$2n+1\le \frac{2}{0.15}$
$2n+1\le 13$
$\Rightarrow n\le 6$
$\therefore n=0$ to $n=6\Rightarrow 7$ resonances