SOUND

There are three stations to visit during this lab. Each station focuses on a different wave characteristic. Although sound waves are being used, you will study these same characteristics of electromagnetic waves later in the semester.

A. Standing Waves and the Speed of Sound

The resonance tube apparatus, shown to the right, consists of a tube opened at the top end and closed by water at the bottom end. The effective length of this closed-end tube can be changed by adjusting the position of the water reservoir. A tuning fork is struck and held near the top of the tube. The water reservoir is moved until resonance is achieved. Ruler markings on the tube itself can be used to locate positions of resonance.

Procedure:

  1. Select a tuning fork in the range of 400 Hz to 800 Hz. Place the reservoir at the highest level.
  2. Strike the tuning fork with the rubber mallet (never on anything hard) and hold it over the top end of the tube. Quickly lower the reservoir to the bottom. As the water level falls, make note of the water level where resonances occur. The resonances are identified by a sudden increase in the sound level coming from the tube. You should be able to find at least two resonance points.
  3. Move the rubber bands that are wrapped around the tube to the approximate locations where you detected resonance. Set the reservoir at these locations and repeat the procedure above to more accurately determine the exact positions of resonance.
  4. Place a thermometer inside the tube and note the temperature.

Report:

Resonance occurs in a closed-end tube when there is a node at the closed end and an antilnode at the open end. This occurs for a given wavelength l when the effective tube length is 1/4, 3/4, 5/4, etc of the wavelength. The effective length is not exactly the length of the tube, since the last antinode does not occur exactly at the open end. But this correction can avoided by noting that the difference in length between two adjacent resonant lengths is exactly one-half of a wavelngth.

  1. Calculate the difference in the water levels between the two adjacent resonant points. The difference should be one-half of a wavelength. (If you were able to obtain 3 resonant points, calculate the difference between the outer points and use that value as a full wavelength.)
  2. Using the frequency embossed on the tuning fork, calculate the speed of sound.
  3. Calculate the theoretical value using the formula from your text

    v = 331 (1+T/273) m/s

    where T is measured in degrees Celsuis.

  4. Compare your experimental value to the theoretical value. Be sure to include an error estimate for the experimental value based upon the uncertainty in the recorded positions and the recorded temperature.

B. Interference and Wavelength

The total displacement created by two or more waves in a medium is simply the sum of the individual displacements. For two identical periodic sources, this gives rise to an interference pattern with locations of constructive and destructive interference. In this experiment you will use two speakers driven by the same sound generator to create an interference pattern. At places of constructive interference, the sound will be loud, while at places of destructive interference the sound level will be low.

Procedure:

  1. Place the speakers about 6-8 ft apart along a line, facing perpendicular to the line. Connect the two leads from the sound generator to the two screw posts on each speakers, making sure that the same screw post on each speaker is connected to the same generator lead. (You can verify this by standing midway between the speakers. The sound should be loud. If not, reverse the leads on one of the speakers and check again.)
  2. Set the frequency of the generator to approximately 500 Hz and be certain that it is set to generate a sine wave. (The square and sawtooth wave options do not work as well.)
  3. Mark a line about 10 ft away from and parallel to the line of the speakers. Walk along this line and note at least three locations of constuctive interference. (One of your locations of constructive intereference should be at the midpoint, equi-distant from each speaker.)
  4. Measure the distance from each of these locations to each speaker.
  5. Record the temperature in the region where you performed the experiment.

Report:

  1. Calculate the difference in the distance to each speaker for each of the three positions where you found constructive interference.
  2. Calculate the wavelength using the mesurements above. Note that the location of the midpoint of constructive interference should lie equidistant from each speaker. If it does not, you should use the difference to adjust the calculations made for the other two locations, if appropriate, and use it in the error estimate. Be sure to explain how you used these measurements to deduce the wavelength.
  3. Calculate the frequency using your calculated wavelength and the speed of sound in the region of the experiment. (Utilize the temperature-dependent speed formula used in the previous section.) Compare your value with that on the generator display.

C. Beats

Beats are an interference phenomenum which occurs from the addition of two (or more) waves of different frequencies. Unlike the previous experiment, the interference pattern varies in time, as well as space. In the case of two different frequencies of roughly equal amplitude, the listener will note that the loudness of the sound "wavers". This occurs as the two sound waves interfere constructively and destructively. The frequency of the beats is equal to the difference of two frequencies.

Procedure:

  1. Connect the microphone to the oscilloscope. Connect each frequency generators to a speaker. Place the two speakers at about 45o such that they face the microphone.
    At this point, you should turn off the generator and try "singing" into the microphone, changing both pitch and volume until you understand how frequency and volume correlate to the oscilloscope display.
  2. Set the frequency of one of the generators to about 250 Hz. With only this generator operating, set the oscilloscope time sweep such that you see at least 10 oscillations, around 50 ms. Adjust the channel horizontal position and the calibration on the time sweep (red knob in the center) until 10 oscillations fit perfectly within the nearest major divisions. Using the frequency displayed on the generator, you will be able to determine the time scale of the oscilloscope display. Your instructor will help you through the procedure.
  3. Turn on both generators and fine-adjust them until the same frequency is displayed. Watch the behavior of the waveform on the oscillscope and note how it correlates to what you hear. Ideally, you should hear no beats for identical frequencies. However, the generators are not perfect and you should be able to both see and hear low frequency beats as the generators drift into and out of constructive interference. Using a stopwatch, estimate the frequency of the beats. This will give you an estimate of the frequency error of the generators.
  4. Increase the frequency of one of the generators until you can see one envelope of the beat frequency. It will require some some fine tuning to keep the envelope from drifting. Once it is stable, count the number of divisions spanned by the envelope and record both frequencies on the generators.

Report:

  1. Determine the time scale of the oscilloscope by dividing the time of 10 oscillations (10 times the reciprocal of the frequency) by the number of divisions spanned by 10 oscillations that you measured in step 3 of the procedure.
  2. Using the time scale from the previous step, determine the beat period and frequency from the number of divisions spanned by the beat envelope in the last step of the procedure.
  3. Compare the beat frequency to the difference in the generator frequencies. Are they the same within the frequency error of the generators?