A tuning fork of frequency 340Hz is vibrated just above a cylindrical tube of height 1.2m. If water is slowly poured into the tube; at what maximum height will resonance occur. [speed of sound in air = 340ms−¹]

A. 0.95m
B. 0.60m
C. 0.50m
D. 0.45m

Correct Answer:

Option D – 0.45m

Explanation

In vibration in a closed pipe/tube, the first resonance occurs at a position L = ^V/_4f,
when reading from the top of the tube,

L₁ =	_340
	4 x 340

= 0.25m
L₂ = ^3V/_4f

L₂ =	3 x 340
	4 x 340

= 0.75m
L₃ = ^5V/_4f

L₃ =	5 x 340
	4 x 340

= 1.25m
However, the effective length of the tube is 1.2m. Thus reading from below, the first position of resonance will be 1.20 – 0.75m = 0.45m