Experiment: To determine (i) the wavelength of sound produced in an air column, (ii) the velocity of sound in air at room temperature using a resonance column and a tuning fork.
Air columns in pipes or tubes of fixed lengths have their specific natural frequencies. For example, in a closed organ pipe (closed at one end) of length Lt when the air column is set into vibration with a tuning fork of a particular frequency, it vibrates in resonance with the tuning fork. The superposition of the waves travelling down the tube and the reflected waves travelling up the tube produce (longitudinal) standing waves which must have a node at the closed end of the tube and an antinode at the open end.
The resonance frequencies of a pipe or tube (air column) depend on its length L. Only a certain number of wavelengths can be fitted into the tube given the condition that there should be a node at the closed end and an anti-node at the open end. But the distance between a node and an anti-node is λ/4 and therefore, resonance occurs when the length of the tube (air column) is nearly equal to an odd number of λ/4.
L = λ/4, 3λ/4, 5λ/4, ...
L = nλ/4 where n = 1, 3, 5, ...
where λ is the wavelength of the sound. The relation between the wavelength and frequency of the sound source is:
v = f λ
For a closed pipe,
fn = nv/4L where n = 1, 3, 5, ...
The lowest frequency (n = 1) is called the fundamental frequency and higher frequencies are called overtones. Hence, an air column of length L has particular resonance frequencies and will be in resonance with the corresponding driving frequencies.
The three parameters involved in the resonance condition of an air column are f, v and L. To study resonance in this experiment, the length L of the air column will be varied for a given driving frequency (the wave velocity in air is relatively constant).
The difference in the tube (air column) lengths for successive condition of resonance is
ΔL = L2 - L1 = 3λ/4 - λ/4 = λ/2
λ = 2ΔL
You can determine the wavelength of sound waves by measuring ΔL. Then by knowing frequency f of the driving tuning fork, the velocity of sound in air at room temperature can be calculated using the relation:
Δv = fλ = 2f(L2 – L1)
Resonance tube apparatus, tuning forks, rubber mallet or block, meter stick (if measurement scale not on resonance tube) and thermometer
1. Note the room temperature.
2. Note the frequency of the tuning forks.
3. Set the resonance tube apparatus in vertical position with the help of levelling screws attached to its base and spirit level. Fill the reservoir with water and raise it to adjust the water level in the long tube to a point near the top. Do not overfill the reservoir otherwise it will overflow when you lower it. Practice lowering and raising the water level
in the tube to get the “feel” of the apparatus.
4. With the water level in the tube near the top, take the tuning fork and set it into oscillations by striking it with a rubber mallet or on a rubber block, whichever is available. Never strike the tuning fork on a hard object (e.g. a table). This may damage the fork and cause a change in its characteristic frequency. Hold the vibrating fork horizontally slightly above the opening of the tube so that the sound is directed down the tube. (Note that a tuning fork has directional sound-propagation characteristics. Experiment with a vibrating fork and your ear, to determine these directional characteristics).
5. Lower the reservoir to a low position on the support rod. Adjust the water level in the tube to fall in steps of 1 cm, controlling it with the help of pinch cork. Bring the tuning fork at top of the tube each time. Continue till a loud sound is heard.
6. Now raising and lowering the water level in steps of 1 mm try to locate the position at which maximum sound is heard. This is first resonance position.
7. Determine the exact position of the water level on the scale, (while noting the position, measure the length from the top of the tube) for the first resonance. Repeat the experiment thrice.
8. Repeat this procedure for the second resonance position, at around three times the length of air column for first resonance.
9. Compute the average lengths of air column for first and second resonances. Then compute wavelength from the difference between them. Using the known frequency of the fork, calculate the velocity of sound.