Question

A tuning fork of frequency $330\, Hz$ resonates with an air column of length $120 \,cm$ 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 $ 330\text{ }m{{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 $=340 m / s$
$V=$ frequency $=340 H _{2}$
also
$
\begin{aligned}
V=\nu \lambda \text { OR } \lambda &=\frac{V}{V} \\
&=\frac{340}{340}=1 m
\end{aligned}
$
first resonating length,
$
l_{1}=\frac{\lambda}{4}=\frac{1}{4} m=25 cm
$
second resonating length,
$
l_{2}=\frac{3 \lambda}{4}=\frac{3 \times 1}{4}=75 cm
$
Thind resonating length,
$
l_{3}=\frac{5 \lambda}{4}=\frac{5 \times 1}{4}=125 cm
$
So third resonance is not possible since the length of the tube is $120 cm$.
$\therefore$ minimum height of water necessary for resonance $=120-75$
$=45 cm$