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Using Waves to Measure the Speed of Sound

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Author: Jerry Silver

The Idea

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

Method

Two speakers/one microphone

  1. 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.
  2. 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.
  3. 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.
  4. 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.)
  5. Display the waveform picked up by the microphones on the oscilloscope. Adjust the amplitude, time scale, and, if needed, the trigger setting.
  6. 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.

    Using Waves To Measure The Speed Of Sound.

  7. 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.
  8. 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).
  9. 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.
  10. 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.)

    Using Waves To Measure The Speed Of Sound.

  11. 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.)
  12. Once we have the wavelength, , and the frequency, f, you can multiply them together to get the velocity using the wave equation:

    v = f

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