A turning 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
Verified Correct Answer: A.
Physical Principles & Numerical Solution
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,
L\(_1\) = \(\frac{340}{4 \times 340}\) = 0.25m
= 0.25m
L\(_2\) = \(\frac{3V}{4f}\)
L\(_2\) = \(\frac{3 \times 340}{4 \times 340}\)
= 0.75m
L\(_3\) = \(\frac{5V}{4f}\)
L\(_3\) = \(\frac{5\times 340}{4\times 340}\)
= 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 - 0.25m = 0.95m
Source: Myschool Past Questions Archive (Record #12276)