Lab: Sound Waves and Beats

Lab: Sound Waves and Beats

Sound Waves and Beats

Purpose:        Measure the frequency and period of sound waves.
        Measure the amplitude of sound waves.
        Observe beats between the sounds of two sound sources.

Background:Sound waves consist of a series of air pressure variations. A microphone diaphragm records these variations by moving in response to the pressure changes. The diaphragm motion is then converted to an electrical signal. Using a microphone, you can explore the properties of common sounds.
        The first property you will measure is the period, or the time for one complete cycle of repetition. Since period is a time measurement, it is usually written as T. The reciprocal of the period (1/T) is called the frequency, f, the number of complete cycles per second. Frequency is measured in hertz (Hz). 1 Hz = 1 s–1.
        A second property of sound is the amplitude. As the pressure varies, it goes above and below the average pressure in the room. The maximum variation above or below the pressure mid-point is called the amplitude. The amplitude of a sound is closely related to its loudness.
        In analyzing your data, you will see how well a sine function model fits the data. The displacement of the particles in the medium carrying a periodic wave can be modeled with a sinusoidal function.
In the case of sound, a longitudinal wave, the y refers to the change in air pressure that makes up the wave. A is the amplitude of the wave (a measure of loudness), and f is the frequency. Time is represented with t, and the sine function requires a factor of 2?when evaluated in radians.
        When two sound waves overlap, air pressure variations will combine. For sound waves, this combination is additive. We say that sound follows the principle of linear superposition. Beats are an example of superposition. Two sounds of nearly the same frequency will create a distinctive variation of sound amplitude, which we call beats.

  • Set up the LabQuest to use its internal microphone: click on Sensors and Sensor Setup. Check the box beside Microphone and then click on OK.
  • Pick two tuning forks that are one note apart (a D and an E for example). Produce a sound with one of the tuning forks (hit the tuning fork only on a soft surface such as a rubber stopper) and hold it close to the microphone on the LabQuest. (This is the little hole near the Vernier LabQuest label on the LabQuest.) Start data collection. If you get a really rough graph, try again until you get something fairly smooth. Record this as Run 1 by clicking on the little Filing Cabinet icon next to where it says Run 1. Sketch this graph in your lab notebook.
  • Now try to get a smooth graph with the second tuning fork and save it as Run 2. Sketch this graph in your lab notebook, too.
  • Since it isn’t easy creating smooth graphs with the tuning forks, we will use a single frequency sound source for our other trials. Visit the website to generate the wave. For Frequency, use the frequency of your first tuning fork. Duration should be anywhere from 3 to 10 seconds. The level is probably fine left where it is but can be changed if the website gives you an error message. The default sample rate is also fine.
  • The file will now download to your netbook. Hook a set of headphones to your netbook and listen to the generated tone. It should be the same tone as your tuning fork but without all of the overtones. Position one of the headphones over the LabQuest microphone and try collecting a smooth graph using this sound source. Save it as Run 3. Sketch this graph in your lab notebook.
  • To examine the data pairs on the displayed graph, tap any data point. As you tap each data point, sound and time values will be displayed to the right of the graph. Record the times for the first and last peaks of the waveform. Record the number of complete cycles that occur between your first measured time and the last. Divide the difference, Delta t, by the number of cycles to determine the period of the tuning fork. Record the period in your data table.
  • Use the period you just determined to calculate the frequency of the sound source in Hz and record it in your data table. How close is that to the frequency you actually used?
  • Examine the graph again, and record in your data table the maximum and minimum sound values for an adjacent peak and trough.
  • Calculate the amplitude of the wave by taking half of the difference between the maximum and minimum y values. Record the values in your data table.
  • Use the same website to generate a wave file that has the same frequency as your second tuning fork. Once the data is collected for this tone, save it as Run 4. Determine the period, frequency, and amplitude for this wave as you did the other.
  • Save this file as X-X-Waves. Then create a new file. Turn on the internal microphone sensor again and this time change the duration to 0.08s.
  • For this part of the experiment we will create beats using the two different tones. You can listen to the beats produced by your two tuning forks by activating them simultaneously. In your notebook describe what you observe.
  • Visit the website in order to generate the dual tone wave source. Type in the two frequencies of your two tuning forks, and choose the same level for each (-10dBFS is a good start). Again choose a duration between 3 and 10 s. Download this file and try to record a good wave function.
  • Sketch the shape of your waveform graph. You should see a time variation of the sound amplitude. The pattern will be complex, with a slower variation of amplitude on top of a more rapid variation. Ignoring the more rapid variation and concentrating in the overall pattern, count the number of amplitude maxima after the first maximum and record it in the data table.
  • Record the times for the first and last amplitude maxima. To do this, tap any data point. Divide the difference, Delta t, by the number of cycles to determine the period of beats (in s). Calculate the beat frequency in Hz from the beat period. Record these values in your data table.
  • Save this LabQuest file as X-X-Beats.

  • Open your X-X-Waves file either with the LabQuest or on your netbook in LoggerPro. Go to Run 3. Fit a sine curve to this graph by going to Analyze then Curve Fit. Choose “Sine” from the list. If your data is clear, you should get a near-perfect fit. Record the values for A and B for this graph. Then analyze Run 4 in a similar manner and record its A and B values.
  • Since the model parameter B corresponds to 2?f (i.e., f = B/(2?)), use your fitted model to determine the frequency for Run 3. Enter the value in your data table. Compare this frequency to the frequency calculated earlier. Which would you expect to be more accurate? Why? Repeat for Run 4.
  • Compare the parameter A to the amplitude of the waveform for both Run 3 and Run 4. Ideally these values would be the same. Are they? Why or why not?
  • For your Beats data, compare the beat frequency to the two frequencies you played together. Is there any way the two individual frequencies can be combined to give the beat frequency you measured earlier? Compare your conclusion with information given in your textbook.
Lab Write-Up
        For this lab, you will simply have the data you collected in your lab notebook along with the analysis above, also in your lab notebook. Then your group should turn in the two graph files which you created. Upload the data into Logger Pro and save with the same names as their LabQuest files. Then copy them into the Turn In folder. There is no lab report to type for this experiment.
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