Question

A tuning fork of frequency $330Hz$ resonates with an air column of length $120cm$ in a cylindrical tube, in the fundamental mode. When water is slowly poured in it, the minimum height of water required for observing resonance once again is
(Velocity of sound $330m{s}^{-1}$ )

• A. 75 cm
• B. 60 cm
• C. 50 cm
• D. 30 cm
• E. 45 cm

Answer 1

Answer: (E)

We know that,
$V=$ speed of sound in air $=340m/s$
$V=$ frequency $=340H_2$
also
$<br/>\begin{array}{rl}<br/>V=\nu \lambda \text{ OR }\lambda & =\frac{V}{V}\\ <br/>& =\frac{340}{340}=1m<br/>\end{array}<br/>$
first resonating length,
$<br/>l_1=\frac{\lambda }{4}=\frac{1}{4}m=25cm<br/>$
second resonating length,
$<br/>l_2=\frac{3\lambda }{4}=\frac{3\times 1}{4}=75cm<br/>$
Thind resonating length,
$<br/>l_3=\frac{5\lambda }{4}=\frac{5\times 1}{4}=125cm<br/>$
So third resonance is not possible since the length of the tube is $120cm$.
$\therefore$ minimum height of water necessary for resonance $=120-75$
$=45cm$