Sound Waves
Introduction
Sound waves are vibrations that propagate through a medium such as air. In this lab, you will
investigate several properties of sound, such as pitch, octaves, beat frequencies, overtones, and the
frequency limits of human hearing.
Skip the error estimations and error propagation for this particular experiment.
Experimental Procedures
Audacity
1) Run the program “Audacity” on a computer. You may choose to download and install it on
your own computer as it is free: http://audacity.sourceforge.net/
Frequency and Period
2) Generate a 220 Hz sine wave and calculate theoretical and experimental period.
a. Click on “Generate” and “Tone”.
b. Select “Sine” for the “Waveform”.
c. Change the frequency to 220 Hz.
d. Change the length to 2.0 seconds.
e. Click on the “Generate Tone” button.
f. Calculate the theoretical period using T = 1/f.
g. Click repeatedly on the magnifying glass with a “+” sign until about 1 cycle is visible.
h. Measure the locations of two adjacent peaks or troughs.
i. Calculate the experimental period by measuring the time between adjacent peaks or
troughs.
j. Compare the experimental and theoretical periods.
Pitch and Frequency Ratios
3) Generate an additional 440 Hz sine wave with a time delay.
k. Click on the “Selection Tool” in the upper left corner.
l. Click on the empty space below the 220 Hz sine wave.
m. Click on “Generate” and “Silence”.
n. Change the length to 2.0 seconds.
o. Click on the very end of the track with silence.
p. Click on “Generate” and “Tone”
q. Select “Sine” for the “Waveform”.
r. Change the frequency to 440 Hz.
s. Change the length to 2.0 seconds.
t. Click on the “Generate Tone” button.
4) Click on the green play button and listen to the tones in sequence. Compare the two sounds
and record your observations. Note that this is a frequency ratio of 2:1 and is called an
“octave.” Both of these are considered “A” notes and are generally observed to be pleasant
when observed in sequence.
5) Try pairs of frequencies in sequence with ratios of 3:2 (a “fifth”), 5:4 (a “major third”), √2:1
(“augmented fourth”) and 21/12:1 (a “half-step”). Record your observations. The first two are
generally observed to be pleasant in sequence while the last two are not.
Note: do not play more than one frequency at a time. The term “in sequence” means that you do not
play the two frequencies at the same time. It means that you play one after the other (hence the delay
for the second tone). You will not receive full credit on your report if you ignore this.
Beats
6) Delete any existing tracks.
7) Generate a 220 Hz sine wave.
8) Click on “Project” and “New Audio Track”
9) Generate a 221 Hz sine wave.
10) Click on the green “play” button and listen. The oscillation in volume is called a “beat”. Record
your observations.
11) Click “pause” when the sound is loud. Zoom in on the oscillations and compare them.
12) Click “play” and then “pause” when the sound is soft. Compare the two oscillations.
13) Delete both tracks when you are done.
Listening to Awesome
14) Click on the link labeled “awesome sound”. Record your observations.
Instruments, Spectra, and Overtones
15) Right-click and save the “fiddle”, “flute”, “singer” and “drum” sounds.
16) Click “File” and “Open” in Audacity. Choose one of the sounds.
17) Click the play button.
18) Click and drag your cursor over a large portion of the wave.
19) Click on “Analyze” and “Plot Spectrum”.
20) Change the resolution to 1024.
21) Find the fundamental frequency.
a. Move your cursor over the first large peak. This is usually, but not always, the biggest.
b. Record the fundamental frequency and dB level.
22) Find all overtones.
a. Move your cursor over several other large peaks.
b. Record the frequencies and dB levels.
c. Calculate the ratios of the frequencies of the overtones to the fundamental frequency.
DO NOT calculate the ratios of the fundamental frequency to the frequencies of the
overtones. If you do not understand this distinction, then please see the following
webpage: http://en.wikipedia.org/wiki/Ratio
d. Test the theory that the ratios are whole numbers.
23) Click on the “x” in the upper left corner of the audio track to delete it.
24) Repeat steps 16 through 23 for all sounds.
Frequency Limits of Human Hearing
25) Gather a group of people if possible to test their hearing.
26) Generate and listen to an 8000 Hz sine wave for 0.10 seconds. Keep the volume reasonably
low and don’t put your ears near the speakers even if you can’t hear it. Note the age of anyone
who can’t hear the sound.
27) Delete the previous track and increase the frequency by 500 or 1000 Hz at a time. Note the age
and maximum frequency observed for each participant.
28) Share and use data on the discussion board so that you have 15 or more data points.
29) Graph the maximum frequency observed as a function of age and note any trends. Don’t even
think about putting in a gratuitous trend line.