Question

A tuning fork of frequency $330\text{Hz}$ is vibrated just above the tube of $100\text{cm}$ height. Water is poured slowly in the tube. What is the minimum height of water necessary for the resonance?

$[$Take speed of sound $=330\text{m/s}]$

• A. $40\text{cm}$
• B. $35\text{cm}$
• C. $30\text{cm}$
• D. $25\text{cm}$

Answer 1

The correct option is D $25\text{cm}$

Given,
Frequency of tuning fork $f=330\text{Hz}$
Height of the tube $H=100\text{cm}$

We know that $v=f\lambda$

$\Rightarrow \lambda =\frac{v}{f}=\frac{330}{330}=1\text{m}$

For a closed organ pipe (organ pipe filled with water), it's fundamental resonating length,

$l_1=\frac{\lambda }{4}=\frac{1}{4}\text{m}\text{or}25\text{cm}$

Second resonating length,
$l_2=\frac{3\lambda }{4}=\frac{3}{4}\text{m}\text{or}75\text{cm}$

Third resonating length,
$l_3=\frac{5\lambda }{4}=\frac{5}{4}\text{m}\text{or}125\text{cm}$

Third resonance is not possible because the length of tube is only $100\text{cm}$.

$\therefore$ Minimum height of water necessary for resonance,
$H_{min}=100-75=25\text{cm}$

Thus, option (d) is the correct answer.