RESONANCE TUBE

By Aditya Abeysinghe

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Resonance tube is either an open ended or close ended tube which is used to examine the characteristics and resonance lengths to different frequencies of other close ended or open ended tubes.

Resonance occurs when an oscillating system is made to oscillate ,from an outside source, at a frequency which is the same as its own natural frequency.

WHAT IS A RESONANCE TUBE?

We perform the experiment as to how the resonance tube acts as a closed tube by drowning the tube in water, so that the end which was drowned in water acts as a closed end.

See diagram below.

RESONANCE TUBE AS A CLOSED TUBE

Beaker

Water

Resonance tube

Open end

Closed end

Cotton wool or sand (to prevent the sound waves from reflecting)

You know that at the close end a node should be formed and at the open end an antinode should be formed.

Objective: The objective of this experiment is to find the length of the resonance tube at which resonance occurs.

We’ll take the same set up to do the experiment.

See figure below.

THE EXPERIMENT

Beaker

Water

Resonance tube

Open end

Closed end

Cotton wool or sand (to prevent the sound waves from reflecting)

Tuning folk

If the frequency at which the tuning folk is oscillating is f, the minimum length of the resonance tube at the time of resonance is l, the end correction is e, the wave length of the wave formed due to the oscillation of air inside the tube is λ and the speed of sound in air is V,

Then,e

l

λ/4 = l + e. Therefore, λ = 4(l+e)

However, V = f λ. Therefore, V = f× 4(l+e)

Thus, l = (V/4)f – e

This graph is in the form of y = mx – c

The gradient of the graph, m = V/4So, the speed of sound in air = 4mAlso, the intercept, c = -eBy this we can also find the end correction of the tube.

Method:

1. Set up the apparatus as shown.

2. Take the tuning folk that oscillated with the highest frequency and oscillate it.

3. Then gradually lift the tube until a high sound is heard. This is the first resonance of the experiment.

4. Measure the length, at that instance, from the upper level of water to the open end of the tube.

5. Verify that this length is the least length at which the first resonance occurs. This can be examined by lowering the tube and observing whether another high sound can be heard at some length.

6. Record the resonance lengths for different tuning folks. When selecting tuning folks, it should be noted that they should be selected on the sequence of the decresing order of their frequencies.

7. Use a thermometer to find the room temperature. Because the value you get for the speed of sound in air is at that temperature.

Important:

The air inside the tube will be saturated by water vapor during the experiment. Thus, the observed speed of sound in air is larger than the expected value at that temperature.

Since an experiment cannot be performed to find the resonance length for an open tube by drowning in water, it should be evident that the experiment should be done in the air.

Thus, the wave form for such an experiment is as follows:

RESONANCE TUBE AS AN OPEN TUBE

l

Node

Antinode

e e

However, when performing the experiment in air, it’s hard to do this with a single tube. So, what we do is that we use two tubes as follows and change the lenghts of the tubes.

For the open tube,

λ / 2 = l + 2e . Also, λ = V / f. Therefore, l + 2e = V / 2 f

Therefore, l = (V / 2)(1/f) – 2e

This is in the form of y = mx – c, where the gradient is V/2 and the intercept is -2e

Tube 1Tube 2

Merge rod

Method:

1. Arrange the tubes as shown and fix them to a G clamp so that the two tubes are parallel to the table.

2. Oscillate the tuning folk with the highest frequency and hold it perpendicularly to an open end.

3. Change the length of the tube until a high sound is heard and record this length.

4. Verify that this length is the least length at which the first resonance occurs. This can be examined by decreasing the length of the tube and observing whether another high sound can be heard at some length.

6. Record the resonance lengths for different tuning folks. When selecting tuning folks, it should be noted that they should be selected on the sequence of the decresing order of their frequencies.

7. Use a thermometer to find the room temperature. Because the value you get for the speed of sound in air is at that temperature.

The gradient of the graph, m = V / 2.

So, the speed of sound in air = V = 2m

Also, the intercept of the graph, c = 2e

Therefore, the end correction of the tube, e = c / 2