Name _________________________________________
Date ______________ Lab Time _________________
Lab TA _______________________________________
PHYSICS 116
THE SPEED OF WAVES
Purpose
To measure the speed of waves in two different media.
I. For the speed of sound in air, you will use a speaker and microphone in a tube, connected to a
computer signal generator and data acquisition system.
II. For the speed of waves on a string, you will use a string of fixed length and variable tension,
driven by a computer signal generator.
These are two independent parts, so you can do them in any order.
Apparatus
Part I: Computer, Pasco Science Workshop 850 Universal Interface, speaker (attached to a meter stick) and
microphone enclosed in a long tube, Pasco BNC adapter, BNC to miniature phone jack cable (for
microphone), and two 4-foot banana leads.
Part II: Computer, Pasco Science Workshop 850 Universal Interface, two 4-foot banana leads, brass weight
set, meter stick, and vibrating string apparatus.
Part I. Speed of Sound in Air
The most straightforward method of determining the speed of sound in air is to measure the time it takes for
a sound pulse to travel over a known distance. An alternative way is to make use of the relation between the
speed of sound, the wavelength of the sound wave and the frequency of the wave source.
The oscilloscope is ideally suited for the determination of the speed of sound in air in the laboratory. You
will use two different oscilloscope methods and compare their relative merits. In this experiment today, we
will use a computer with a data acquisition interface and a virtual oscilloscope program that is a module of
Capstone.
DESCRIPTION OF METHODS: Consider the diagram in Fig. 1. It represents the instantaneous picture of
a simple sound wave emitted in the axial direction by a sound source S (e.g., a speaker). Note that the air
molecules at M1 and M3 have the same phase as those at S, whereas those at M2 are 180 out of phase.
Therefore, if one places a microphone at position M1, the pressure variations (with time) as indicated by the
microphone will be in phase with the pressure variations at the speaker S. Now suppose we move the
microphone slowly from position M1 to a new position M3. The output from the microphone is then again
in phase with that from the speaker ─ we have reproduced the same situation as before. The distance the
Physics 116
The Speed of Waves
M. From/M. Knittel
Fall 2015
Page 1.
microphone had to be moved to achieve this is one wavelength . (In the actual experiment, it is the speaker
that is moved; the microphone is stationary).
The in-phase position of the microphone may be found either by using a dual-trace oscilloscope to display
speaker and microphone outputs on separate channels (METHOD 1), or by making use of Lissajous figures;
i.e., by feeding the speaker output into the Y-axis and the microphone into the X-axis of an oscilloscope
(METHOD 2). Knowing the frequency f of the sound source, the speed of sound v in air may be calculated
from the equation
v f
(1)
Figure 1. Instantaneous Picture of a Simple Sound Wave.
Note that we are dealing with travelling sound waves and not standing waves. Although the generation of
some standing waves in a closed tube is unavoidable, they should have no serious effect on the experiment.
The closed plastic tubes are used to keep your signals from interfering with other students' experiments.
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Physics 116
The Speed of Waves
M. From/M. Knittel
Fall 2015.
Procedure for Part I
With red and black banana plug leads, connect the Pasco
850 Interface signal generator OUTPUT 1 to the speaker
input binding posts on the speed of sound tube. The
signal generator output is automatically and internally
connected to Ch O1 of the oscilloscope.
Using the Pasco BNC adapter and the BNC to miniature
phone jack cable connect the microphone to the Pasco
850 Interface ANALOG INPUT A. The microphone
signal will be displayed on Ch A.
METHOD 1. USING A DUAL-TRACE OSCILLOSCOPE
1. Turn on the PASCO 850 Interface and the microphone in-line amplifier.
2. Sign in to your computer.
3. Double click on the Capstone icon near the upper-left side of the desktop.
4. Click on the “Open Experiment”
button, second from the left on the
toolbar.
5. In the left pane, select
“K-Drive (K:)”
Browse to
“Physics\P116\Speed of Waves”
Select “Speed of Sound 2
Channel.cap” and click on <Open>
6. Your screen should look like this—but
empty of data.
The right side of the display is the oscilloscope screen, showing the amplitude of the two waves as a
function of time. The amplitude of the signal generator Ch O1 is read from the left-hand scale. The
amplitude of the microphone signal Ch A is read from the right-hand scale.
Physics 116
The Speed of Waves
M. From/M. Knittel
Fall 2015
Page 3.
The left side of the display is the control panel for the signal generator.
7. First, click on the Monitor button at the bottom left of the window. This will start the oscilloscope.
Second, click on the Signal Generator
On button.
You should now hear—and see on the
oscilloscope—the 3500 Hz sine wave.
8. Beginning with the meter stick pushed
into the tube so that the speaker is about
10 cm from the microphone, change the
distance between the microphone and
the speaker by slowly pulling out the
meter stick. Because both signals on the
oscilloscope screen are triggered by the
signal into Ch O1, the microphone
signal display (Ch A) should move
sideways, while the loudspeaker input
signal display (Ch O1) should remain
stationary.
Since not all microphones may be created equal, you may find the need to adjust
the display amplitude of the microphone signal. Click in the right-hand
oscilloscope scale for Ch A. The cursor will become a double-headed arrow
which you can drag up or down to adjust the display.
9. With the microphone-to-speaker distance returned back to about 10 cm, adjust
the speaker position until the two signals are exactly in phase. Then move the
speaker out until the two signals are again exactly in phase. The distance
through which the speaker has moved is exactly one wavelength of the sound
waves transmitted through the air. Continue to pull out the meter stick,
increasing the distance between the microphone and the speaker. Each time the
two signals are exactly in phase, note the speaker position. In this way, obtain
several values for the wavelength .
10. Click on Off.
From your  values calculate the average value of  and estimate the uncertainty, , in . (A rough
estimate of the uncertainty is simply half the difference between your largest and smallest  values.) Then
use equation 1 along with your values for  and f to calculate your observed velocity of sound waves in air.
𝒗 = _________. Finally, calculate the uncertainty, ∆𝑣, in your value of 𝑣 by using the following equation:
    f 
v  v 

    f 
2
2
(2)
You may assume a 1% uncertainty in the oscillator frequency f/f. That is, in the ∆𝑣 equation , f/f = .01.
∆𝒗 = ________________. What is the accepted value of the speed of sound in air at standard temperature and
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Physics 116
The Speed of Waves
M. From/M. Knittel
Fall 2015.
pressure? (look this up!) Is your value of 𝑣 ∓ ∆𝑣 in agreement with this accepted value? If not, try to come
up with a possible explanation for the poor agreement.
METHOD 2. USING LISSAJOUS FIGURES
We now wish to use the input to Ch A of the oscilloscope as the X-axis signal (rather than using time).
1. Click on the “Open Experiment” button, second from the left on the toolbar.
<Discard> modifications to the previous experiment.
2. In the left pane, select
“K-Drive (K:)”
Browse to
“Physics\P116\Speed of Waves”
Select “Speed of Sound Lissajous
Figure.cap” and click on <Open>
3. Your screen should look like this—but
empty of data.
4. Again, click on the Monitor button at
the bottom left of the window. This
will start the oscilloscope.
Second, click on the Signal Generator On button.
You should hear the 3500 Hz tone and see a simple Lissajous figure on the oscilloscope screen—its
shape (straight line, ellipse or circle) will depend on the phase difference between and amplitudes of the
X- and Y-signals.
Again, you may find the need to adjust
the display amplitude of the
microphone signal. Click in the
bottom oscilloscope scale for Ch A.
The cursor will become a doubleheaded arrow which you can drag left
or right to adjust the display.
Starting with the meter stick at about 10 cm, increase the distance between the microphone and the
speaker—the Lissajous figure will gradually change shape, a particular figure (e.g., a straight line of
positive slope) repeating itself every time the phase difference changes by 360 (2).
5. Start with the smallest microphone-to-speaker separation which yields a straight line of positive slope
(from lower left to upper right corners of the screen at about 45). Next, slowly increase the separation
until a straight line sloping in the same direction again appears on the screen. The Lissajous figure has
gone through 360, and the distance through which the speaker has moved equals one wavelength of the
Physics 116
The Speed of Waves
M. From/M. Knittel
Fall 2015
Page 5.
sound waves. Continue to increase the distance between the microphone and the speaker, each time
noting the speaker position when the two signals are exactly in phase. In this way obtain several values
of the wavelength .
6. Click on Off.
Treat the data in the same way as in Method 1 to find your value of the speed of sound, 𝑣, and its
uncertainty, ∆𝑣.
𝑣 = __________________ ∓ ___________________
As before, Compare your of value of the speed of sound with the accepted value for the speed of sound in
air.
Don’t forget to turn off the power to all of the equipment, particularly the battery-powered in-line
microphone amplifier.
And Sign Out!
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Physics 116
The Speed of Waves
M. From/M. Knittel
Fall 2015.
Part II. Velocity of waves on a string
Some systems such as a string or air column or drum are capable of vibrating at several different
resonant frequencies. In order to find these natural frequencies, one uses a "driver" whose frequency can
be varied and notes the driver's frequencies at which the system's response is a maximum.
The system of interest here is a string of effect length L = 105 cm under tension supplied by a hanging
mass. In the picture below, the mass is m = 250 gm. The response is the setting up of standing waves on
the string. You are to find several frequencies, fn with n  1,2, 3 for which you see a standing wave,
determine the wavelengths, n on the string and calculate the velocity of the wave from 𝑉𝑛 = 𝑓𝑛 𝜆𝑛 . For a
given tension T = mg, the Vn should be the same within your experimental error. You will do this for
two different hanging masses to determine how the velocity of waves on a string depends on the tension
in the string.
The variable-frequency driver is attached near one end of the string. The frequency of the driver is
controlled by the computer-controlled signal generator built into the Pasco 850 Universal Interface.
We will be using the “Sweep” capability of the signal generator to help locate the frequency of maximum
string response. This means that we will set an initial starting frequency, a final ending frequency, and a
time duration for the signal generator to sweep continuously from initial to final frequency. Your job is to
watch the change in string amplitude as the sweep is occurring and, with some practice, locate the
frequency of maximum response.
Procedure for Part II
1. Turn on the PASCO 850 Interface.
2. Sign in to your computer.
3. Double click on the Capstone icon near the left side of the desktop.
4. Click on the “Open Experiment” button, second from the left on the toolbar.
5. In the left pane, select
“K-Drive (K:)”
Browse to
“Physics\P116\Speed of Waves”
Physics 116
The Speed of Waves
M. From/M. Knittel
Fall 2015
Page 7.
Select “Vibrating
String.cap” and click on
<Open>
6. Your screen should look like
this—but empty of data.
The right side of the display
has a frequency counter at
the top and an oscilloscope
display at the bottom,
showing the driving signal as
a function of time. The left
side is the control panel for
the signal generator.
7. Note the default settings of the signal
generator. The ones of interest are:
Amplitude:
4V
Initial Frequency:
15 Hz
Final Frequency:
30 Hz
8. First, click on the Monitor button at
the bottom left of the window. This
will start the oscilloscope.
Second, click on the Signal Generator
On button.
You should now see the string begin to
vibrate and the oscilloscope show a
slowly-increasing-frequency sine
wave.
At the end of the 20 s sweep duration,
the signal generator will turn off. The
sweep initial and final frequencies
were chosen to be below and above
the resonance frequency, so you should have seen the string amplitude increase until the resonance
frequency is reached and then decrease. This is the lowest frequency at which the string can resonate.
It is called the fundamental frequency, or first harmonic, and is given the symbol f1.
9. Run the frequency sweep a few more times so that you have a good idea of when the maximum
amplitude will be achieved. Now run the sweep and click on the signal generator Off button when
the maximum just occurs. The frequency meter will show the fundamental resonance frequency. Run
the sweep, stopping it at the resonance frequency, another time or two so that you are confident of
your result. Record this frequency and draw a picture of the shape of the string in the table below.
Remember that for the fundamental resonance of a string, 1 = 2L.
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Physics 116
The Speed of Waves
M. From/M. Knittel
Fall 2015.
10. Now, let’s look at higher harmonics fn = nf1. We need to change the initial and final frequencies so
that they surround the expected frequency of the next resonance.
Calculate f2 and appropriately change the Initial Frequency and Final Frequency in the Signal
Generator control panel.
Repeat the procedure you used above to find the resonance frequency and enter the information in the
table below.
11. Go on to find the f3 resonance frequency.
You may need to increase the signal generator Amplitude by a couple of volts to see the higher-order
waveforms, but note that the best results will occur with the lowest driving amplitude.
Hanging mass m in kg =
Frequency fn
Tension T in the string =
String Mode Shape
(Hz)
f1 = _______ Hz

f2 = _______ Hz

f3 = _______Hz

Average velocity ____________________
Physics 116
The Speed of Waves
Wavelength n
Velocity Vn
(m)
(m/s)
Estimate your error in the velocity ___________________
M. From/M. Knittel
Fall 2015
Page 9.
12. Next repeat your measurements with double the hanging mass of your first experiment.
Hanging mass m in kg =
Frequency fn
Tension T in the string =
String Mode Shape
(Hz)
f1 = _______ Hz

f2 = _______ Hz

f3 = _______Hz

Average velocity ____________________
Wavelength n
Velocity Vn
(m)
(m/s)
Estimate your error in the velocity ___________________
Which one of the six statements below, does your experiment support:
1) The velocity of waves on a string is proportional to the tension squared.
2) The velocity of waves on a string is proportional to the tension.
3) The velocity of waves on a string is proportional to the square root of the tension.
4) The velocity of waves on a string is inversely proportional to the square root of the tension,
5) The velocity of waves on a string is inversely proportional to the tension.
6) The velocity of waves on a string is inversely proportional to the tension squared.
Don’t forget to Sign Out!
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Physics 116
The Speed of Waves
M. From/M. Knittel
Fall 2015.