Question

In a resonance tube experiment, a closed organ pipe of length $120\text{cm}$ resonates when tuned with a tuning fork of frequency $340\text{Hz}$. If water is poured in the pipe, then choose the correct option(s): (Given speed of sound in air, $v_{air}=340\text{m/s}$):

• A. Minimum length of water column to have resonance is $45\text{cm}$.
• B. The distance between two successive nodes is $50\text{cm}$.
• C. The maximum length of water column to create resonance is $95\text{cm}$.
• D. The distance between two successive antinodes is $25\text{cm}$.

Answer 1

Answer: (A), (B), (C)

The maximum length of water column to create resonance is $95\text{cm}$.


For initial resonance:
$\lambda =\frac{v_{air}}{f}=\frac{340}{340}=1\text{m}$
(fundamental mode)

So, vibrating length of air column
For fundamental mode: $L_1=\frac{\lambda }{4}=\frac{1}{4}=25\text{cm}$
For first overtone:
$L_2=\frac{3\lambda }{4}=\frac{3}{4}=75\text{cm}$
For second overtone:
$L_3=\frac{5\lambda }{4}=\frac{5}{4}=125\text{cm}$
i.e second overtone does not establish.

$\therefore$ Minimum length of water column to have resonance $=120-75=45\text{cm}$

& maximum length of water column to create resonance $=120-25=95\text{cm}$

Also, distance between two successive nodes/antinodes $=\frac{\lambda }{2}=\frac{1}{2}=50\text{cm}$

Hence, options (a), (b) & (c) are correct.