Question

In a resonance tube experiment, a closed organ pipe of length 120 cm resonates when tuned with a tuning fork of frequency 340 Hz. If water is poured in the pipe then,
(given $V_{air}=340m/s$)

• A. minimum length of water column to have the resonance is 45 cm
• B. the distance between two successive nodes is 50 cm
• C. the maximum length of water column to create the resonance is 95 cm
• D. the maximum length of water column to create the resonance is 120 cm

Answer 1

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

The correct options are
A minimum length of water column to have the resonance is 45 cm
B the distance between two successive nodes is 50 cm
C the maximum length of water column to create the resonance is 95 cm

Wave length $=\frac{v_{air}}{frequency}=\frac{340}{340}=$ $1m$ or $100cm$

Minimum length of $45cm$ water column creates an air length of $75cm$.

$v=\frac{3c}{4L}$ and $\lambda =\frac{4L}{3}$

For this case $L=75cm$, thus $\lambda$ comes out to be $100cm$.

This $45cm$ is the minimum length of water column.

The two nodes are separated by $\frac{2L}{3}$ distance which gives $50cm$.