In this experiment you will determine the speed of sound by measuring how long it takes sound to get from one microphone to another separated by a known distance. This is almost the same thing you did in Project 72. The only difference is that here we use an oscilloscope to measure the difference in time instead of a stopwatch.
You can take advantage of the wave properties of sound to find the distance between the positions where the sound is loudest. This occurs where the sound constructively interferes. This lets you find the wavelength of the sound. Knowing the wavelength and frequency of sound lets you determine its velocity.
This experiment provides an opportunity to explore basic properties of waves in general. The overall techniques used here can, with significant refinements, also be used to measure the speed of light.
What You Need
- 2 speakers
- 2 approximately 6-foot lengths of hookup wire
- tone generator or a single tone wav file played through a computer or digital audio player
- 2 microphones connected to an oscilloscope (or a sensitive sound meter)
- tape measure, meterstick
- quiet room
Two speakers/one microphone
- Connect the tone generator to the two speakers using the hookup wire. Connect the positive terminal of the tone generator to the positive terminal of each of the speakers. The negative terminal of the tone generator is connected to the negative terminals of each of the speakers.
- Position both speakers side-by-side directed toward the microphone. At this point and throughout this measurement, each speaker should have an unobstructed line-of-sight view to the microphone, as shown in Figure 77-1.
- Turn on the tone generator. Verify that both speakers are functional and at roughly the same volume. You should hear a steady, continuous tone. Any midrange range frequency should work, such as 440 Hz, although this method works well for all audible frequencies.
- Connect the microphone to your oscilloscope. (Alternatively, you can use a sound meter or just listen carefully to determine the positions of maximum and minimum sound intensity.)
- Display the waveform picked up by the microphones on the oscilloscope. Adjust the amplitude, time scale, and, if needed, the trigger setting.
- Slowly move one of the speakers (either forward or back) along the line between it and the microphone. Each speaker should, at all times, continue to face the microphone.
- Monitor the amplitude of the signal displayed on the oscilloscope (or the intensity on the sound sensor; you can also hear the relative intensity of the sound with reasonable accuracy). Be careful to avoid any objects that could block or reflect the sound waves striking the microphone.
- Note the frequency of the sound waves (from the setting on the tone generator or the wav file you used). However, if you don't know the frequency, or just want to confirm it, determine how many seconds it takes on the time scale for one full oscillation to occur. The time it takes for one wavelength to occur is called the period of the sound wave. The reciprocal of the period is the frequency, f (in Hz or cycles per second).
- As you adjust the distance between the speakers, you should see the amplitude of the combined sound waves decrease, reach a minimum, and then return back to its maximum level as the speakers are moved.
- The distance between the speakers when the sound is at a maximumis a full wavelength. This is the result of constructive reinforcement of the signals. The distance between the speakers when the sound is at a minimum is a half wavelength, resulting in destructive interference. (The components for this experiment are shown in Figure 77-2.)
- Measure the distance between the two speakers when the sound is at maximum level. This distance is one full wavelength, , of the sound wave. If you measure this in meters, your calculation for the speed of sound will be in meters per second. (You can get additional data points by measuring different locations, finding the one-half wavelength from the positions when the sound is at a minimum, and then repeating this at various frequencies.)
- Once we have the wavelength, , and the frequency, f, you can multiply them together to get the velocity using the wave equation:
As before, the speed of sound at 20 degrees centigrade is 343 meters per second.
The speed of sound (in meters per second) as a function of temperature (in degrees centigrade) is v = 331 + 0.6T.
Using a 440 Hz tone, the distance separating the microphones to get a 343 meter per second value for the speed of sound is 0.78 meters (78 centimeters).
A 1000 Hz tone would require a 0.343 meter separation to result in the expected value for the speed of sound.
Why It Works
Two waves traveling in the same direction add together to form a new wave. If the crests of the two waves rise at the same time and place, the waves are said to be in phase and reinforce each other to produce a louder sound. This is called constructive interference. This occurs when the two sources of the sound are separated by exactly one full wavelength. (One wave gets a onewavelength head start, but both are in phase at the detector.) If we know the wavelength and the frequency of the sound, we can easily determine its velocity according to the relationship v =
Destructive interference occurs when one wave crests while the trough of a second wave is passing. This happens when the source of the two waves is separated by half a wavelength.
Other Things to Try
Two microphones/one speaker
If you can set up two microphones to your oscilloscope, there is another way to do this that shows the process of interference more clearly. In this case, you follow basically the same procedure as the previous one, except you have one speaker and two microphones. You move the microphones until you observe destructive interference. This occurs when the crest of one wave is at the same place as the trough of the other wave, as shown in Figure 77-3. This method does not work using a sound intensity meter or by listening carefully, as did the previous method.
Following this method, you can use the capability that many oscilloscopes have to detect the point at which the waves are separated by one-half a wavelength. This involves plotting one signal versus the other on the display. When this x versus y plot is a straight line with a slope equal to a negative one, as shown in Figure 77-4, your signals are 180 degrees out of phase and separated by one-half wavelength.
Interference along a line/double slit analogy
Another configuration that can be used to find positions of a constructive and destructive interference is shown in Figure 77-5. This method is analogous to the double slit technique used by Thomas Young with light and is explored in Project 83. The wavelength is given by:
where d is the separation between the speakers and
Speed of light
Using a similar principle, the speed of light can also be measured in the lab. An apparatus is commercially available that determines the wavelength of a known frequency of light by measuring the distance between positions of constructive interference. The measurement is much trickier than the one in this experiment because the speed of light is so much greater than the speed of sound. The same basic approach, however, can be applied to either sound or light.
The speed of sound can be determined if the wavelength and frequency of the wave are known. The wavelength for a given frequency can be determined by finding the distance at which constructive interference occurs.