CUPOL: Acoustic Resonance

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Play all videos at once. [1:23, 18.2 Mb]

Background

The formula for resonant modes of an open tube (i.e., both ends of the tube are open) of length, L, is given by

where l is the wavelength of the sound wave propagating through the tube and d is the diameter of the tube. Note that if we ignore the end correction (by setting d = 0), the above formula becomes the more familiar

Similarly, for a closed tube (i.e., a tube with one open end and one closed end), the equation is given as

where n is the odd integers.

In this experiment, a resonance tube (see Figure 1 below) is used to study acoustic resonance. With this apparatus, one can determine the speed of sound in air, which is given by the formula

Here TC is the temperature in °C and the speed of sound is given in m/s.

Resonance of a closed tube of varying lengths

In this experiment, the resonance tube speaker is being driven by a sinusodial wave function at constant frequency. The input signal is analyzed with an FFT to ensure that it is a pure signal. The speaker-end of the tube is opened. The experimental setup is shown in Figure 1. The function generator is not shown in this picture.

Figure 1. The resonance tube apparatus.

[Click on image to enlarge it.]

A moveable piston is inserted into one end of the resonance tube, thereby closing that end of the tube. As the piston is moved inside the tube, resonances can be easily heard. A microphone is inserted into one end of the tube so the resonances may also be detected by an oscilloscope.

The experiment begins with the piston pushed into the tube so that it is adjecent to the speaker. As mentioned before, the speaker is being driven at a constant frequency. The piston is then slowly moved away from the speaker, effectively increasing the tube length. When a resonance is detected the piston's position is recorded. This is repeated until the piston reaches the opposite end of the tube.

Here are the experimental options and laboratory views that are available to you. Perform as many or as few as you think are necessary.

Play all videos at once. [1:23, 18.2 Mb]

 Resonance tube demonstration. View the movie. [0:15, 3.42 Mb] Open the image. Read the oscilloscope's time scale knob. View the movie. [0:08, 1.51 Mb] Open the image. Speaker input signal. View the movie. [0:08, 1.89 Mb] Open the image. Pinpoint a resonance location. View the movie. [0:17, 3.77 Mb] Open the image. Measure the tube diameter. View the movie. [0:20, 3.68 Mb] Open the image. Measure the room temperature. View the movie. [0:09, 1.81 Mb] Open the image.

The results of the experiment are shown below. When resonance was achieved, the position of the piston (i.e., the tube's length) was recorded.

Length of tube, L
(cm)
3.81
13.71
21.58
33.19
43.02
52.76
62.99
72.00

Use this data along with the above experimetal options to determine
1. The theoretical speed of sound.
2. The wavelength of the sound wave as determined from resonance tube measurements.
3. The experimental speed of sound as determined from resonance tube measurements.
4. The measured tube diameter.
5. The experimental tube diameter as determined from resonance tube measurements.
6. The room temperature determined from the experimental speed of sound.

 Enter TA password to view sample data and results of this experiment (MS Excel format):

If you have a question or comment, send an e-mail to Lab Coordinator: Jerry Hester

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