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 (velocity of sound in air is 340 m/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 45 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


From $v=f\lambda$
$\Rightarrow 340=340\times \lambda \Rightarrow \lambda =1m$
For 1st resonance $l1=\frac{\lambda }{4}$
$\Rightarrow I_1$ = 25 cm so, length of water column is 95 cm
For 2nd resonance $I_2=\frac{3\lambda }{4}=75cm$, so length of water column is (120 - 75) cm = 45 cm
3rd resonance won't be established as for that the length of air column required is $I=\frac{5\lambda }{4}=125cm$ > length of tube
Separation between consecutive nodes is $\frac{\lambda }{2}=50cm$