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
To determine the maximum height at which resonance will occur, we need to find the length of the air column inside the tube that will produce a resonance frequency of 340 Hz.
The formula for the resonant frequency of a closed tube is given by:
fn = (n * v) / (4 * L)
where:
- fn is the resonant frequency
- n is the mode number (1, 2, 3, ...)
- v is the speed of sound in air
- L is the length of the air column
In this case, we want to find the length of the air column that will produce a resonance frequency of 340 Hz. The speed of sound in air is given as 340 m/s, so we can substitute these values into the formula:
340 = (1 * 340) / (4 * L)
Simplifying the equation:
4 * L = 1
L = 1/4
Therefore, the length of the air column that will produce a resonance frequency of 340 Hz is 1/4 of the wavelength of the sound wave. Since the tube has a height of 1.2 m, the maximum height at which resonance will occur is:
1.2 m - 1/4 wavelength
Given that the frequency is 340 Hz and the speed of sound is 340 m/s, the wavelength can be calculated using the formula:
wavelength = speed / frequency
wavelength = 340 m/s / 340 Hz = 1 m
Therefore, the maximum height at which resonance will occur is:
1.2 m - 1/4 m = 0.95 m
So the answer is A. 0.95 m.
To determine the maximum height at which resonance will occur, we need to use the formula for the resonant length of a closed cylindrical tube:
L = (n * speed of sound) / (2 * frequency),
where L is the length of the tube, n is the harmonic number, and frequency is the frequency of the tuning fork.
In this case, the frequency of the turning fork is 340Hz, and the speed of sound in air is 340m/s. We need to find the value of L when resonance occurs, which means n will be the first harmonic, n = 1.
Substituting the values into the formula:
L = (1 * 340) / (2 * 340) = 1/2 meter = 0.50m.
Therefore, the correct answer is C. 0.50m.