Q. A tuning fork of frequency 340 Hz is vibrated just above the tube of 120 cm height. Water is poured slowly in the tube, what is the minimum height of water necessary for the resonance?

A) 45 cm
B) 30 cm
C) 35 cm
D) 25 cm
Explanation

(a) Using relation v=v$\lambda$
Or
$\lambda = \frac{v}{v} = \frac{340}{340} - 1m$
If length of resonance columns are $l_{1},l_{2}and\ l_{3},$ then
$l_{1} = \frac{\lambda}{4} = \frac{1}{4}m = 25\ cm\ \ (for\ first\ resonance)$
$l_{2} = \frac{3\lambda}{4} = 75cm\ \ \ (for\ second\ resonance)$
$l_{3} = \frac{5\lambda}{4} = 125\ cm\ \ \ \ for\ third\ resonance$
This case of third resonance is impossible because total length of the tube is 120 cm
So, minimum height of water =120-75=45cm

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.

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