Lab 1: Introduction to Waves and Sound
OBJECTIVES
To understand how a gaseous system may be characterized by
temperature, pressure, and volume.
To measure the speed of sound waves in air.
To acquire an operational definition of wavelength and frequency.
To introduce standing waves.
To see the standing wave patterns for different situations that lead to
resonances similar to those in various musical instruments. OVERVIEW Figure 1 A wave from throwing
a pebble in a pond Notice the
wavelength between ripples after
you leave the center. (source:
www.avoxtar.com/images/avox
tar_pebble.jpg In the last lab activity you investigated how adding or removing heat
energy to objects either changed the temperature
of the object in question or changed its phase
(melting or boiling for example). In this lab
activity we will begin by looking at the
relationship between pressure, volume, and
temperature of a confined sample of gas.
Next, we will move to waves. Our
emphasis will be sound waves, which are simply
pressure variations that travel through the air.
Many of the things we experience every day are
Figure 2. You can take a snapshot of a wave in time (at
waves: not just water waves on a pond (see figure
1) or ocean, but sound and light itself. A wave
left), to focus on the characteristic wavelength , or you
can measure something in time, at a fixed point (at right),
carries energy and momentum from one place to
to see the characteristic repeat time or “period” T. The
another. In a water or sound wave, this energy is
in the movement of individual water or other
frequency f is defined by f 1/T.
molecules. However, these molecules may stay
almost in place (moving up and down or
backwards and forwards), while the wave itself
moves forward. A simple wave has a
characteristic repetition length, the “wavelength”
(the distance between high points or low
points, for example; see Figure 2), and a
characteristic frequency of oscillation f (cycles
per second.) For anything traveling, we can relate
f and to its speed v by v= f . You can see this
by imagining a wave with wavelength moving
past you at speed v. How many times per second
does a wave crest pass you? This is the
Figure 3 A standing wave on a string (from
“frequency” of the wave. The speed is a
http://www1.union.edu/newmanj/lasers/Light%20as%20a%20Wa
characteristic of the material. Sound in air at
ve/light_as_a_wave.htm). Note that the points that pass through
room temperature and pressure has a speed of
“0” on the left of Figure2 are stationary, and that any snapshots
would see a wave like in that figure, but with different sizes
about 340 m/s.
(Note that at a moment when the string on one side of a noted is
If you place a wave within boundaries
“up, that on the other side is “down”.)
(say, fixing the ends of a string), the wave
bounces back and forth between the ends. This sets up a resonance, where the wave oscillates much more
strongly with particular wavelengths (and thus frequencies.) This kind of wave is called a “standing wave” (See
figure 3.)
p.1 6/4/2013 INVESTIGATION 1: WORK DONE BY A GAS: HEAT ENERGY TRANSFER, INTERNAL
ENERGY, AND THE FIRST LAW OF THERMODYNAMICS
One system we will meet often in our study of thermodynamics is a mass of gas confined in a cylinder with a
movable piston. The use of such a gas-filled cylinder is not surprising since the development of
thermodynamics in the eighteenth and nineteenth centuries was closely tied to the development of the steam
engine, which employed hot steam confined in just such a cylinder.
In thermodynamics we are interested not only in heat energy and work, but in how the two interact. For
example, if we transfer heat energy to a gas, can we get it to do work? In this investigation, you will begin with
some qualitative observations to examine the concept of work done by the gas in a cylinder.
At your lab station you will find a number of syringes that are basically cylinders with movable pistons. By
making some simple observations with these syringes, you can begin to appreciate how an expanding gas can
do work.
You will need
10-mL plastic syringe with the end sealed
Mouse pad
Activity 1-1: Work Done by a Gas in a Cylinder
Try compressing the air in the syringe with the end sealed by pushing the piston (the moveable part that you
usually press on with your thumb) down against the mouse pad on the table. Then let it go, and see what
happens.
Question 1-1: Does it take effort to compress the gas? Do you have to do work on the gas to compress it? (Did
you apply a force over a distance?) What happens when you let go—Does the gas spring back?
In thermodynamics, pressure (defined as the
component of force that is perpendicular to a given
surface for a unit area of that surface) is often a more
x
useful quantity than force alone, since it is
independent of the cross-sectional area of the
cylinder. It can be represented by the equation
F
Piston of crossP
sectional area A
A
moves a distance x.
In the next activity you will explore why pressure
V=A x..
is more useful than force in describing the behavior of
Gas at pressure P
gases. You will also extend the definition of work
exerts a force on the
piston given by F=PA
developed earlier in the course and combine it with
this definition of pressure to calculate the work done
by a gas on its surroundings as it expands out against the piston with a (possibly changing) pressure P.
From your experience with the syringe, do you expect an expanding gas inside a cylinder to do work? You
have probably heard the definition of work in a lecture or seen it in your text. If a force F acts on an object and
the object moves a distance x, the work is W = F x. Using this definition of work and the definition of
pressure, you can show that the work done by a gas on its surroundings as it expands out against the piston with
a (possibly changing) pressure P can be calculated from
W=P V
Question 1-2: Show that the above expression for W follows from W = F x. (Hint: See the preceding
diagram.) Suppose you lift a ball of mass m up from the floor through a distance y. The change in the ball's potential
energy is Ugrav = mgy. The work done by you against the force of gravity is related to the change in the ball's
potential energy so that Ugrav = = - Wgrav. (Keep in mind that the force of gravity on the ball and the
displacement y are vectors.) This relationship is true for any system where mechanical energy is conserved. By
p.2
6/4/2013 doing work against gravity, you are storing energy in the form of potential energy. But what about systems
where mechanical energy is apparently not conserved?
Is it possible to generalize this relationship for some of these systems? The answer is yes, but we have to give
a new meaning to our potential energy. In thermodynamics, U is called the internal energy, and represents any
way of storing energy inside a system. The internal energy of a system is the sum of all sorts of energies,
including the helter-skelter translational kinetic energies of molecules in a gas, the vibrational energies of gas
molecules or atoms in a crystal, and the rotational energies of spinning gas molecules. One way to increase the
internal energy of a system is to transfer heat energy to it as you did when you melted ice or produced steam.
For many materials, the pressure P, volume V, and Temperature T are related to each other through what is
called an “equation of state.” In the next activity, we will exam the relationship between pressure P and volume
V at approximately constant temperature T. First make a prediction.
Prediction 1-1: As you compress the air in a syringe by pushing the piston in slowly, what will happen to the
pressure? What do you think will be the mathematical relationship between pressure P and volume V?
To test your prediction you will need
20-mL plastic syringe (with the needle removed)
computer-based laboratory system
pressure sensor
RealTime Physics Heat and Sound experiment configuration files
Activity 1-2: Isothermal Volume Change for a Gas.
The approach to obtaining measurements is to trap a volume of air in the syringe and then compress the air
slowly to both smaller and larger volumes by pushing or pulling the piston. The gas should be compressed
slowly so it will always have time to come to equilibrium with the room (and thus be at room temperature) You
should take pressure data for about 5 different volumes.
1. Position the piston of the 20-mL syringe at the 10-mL line while the syringe is open to the air, after
positioning the piston connect the end of the syringe to the pressure sensor.
2. Open the experiment file called Pressure vs. Volume (Sound 2A1-2) to display the axes that follow. This
will also set up the software in event mode so that you can continuously measure pressure and decide when
you want to keep a value. Then you can enter the measured volume.
3. Enter the volume of the Pressure sensor, 0.1 cm3, in the second column of Table 1-1.
4. As you pull or squeeze down on the piston slowly, the computer will display the pressure. When the
pressure reading is stable, you can keep that value and then enter the total volume of air from Table 1-1.
5. Repeat this for at least five different volumes of the syringe between 4 and 20 mL.
6. Use the fit routine to find a relationship between P and V.
Table 1-1
Volume of air in
Volume of sensor
Total volume of air in
Pressure
3
3
3
syringe (cm )
(cm )
the system (cm ) 7. Print the graph and attach it. p.3 6/4/2013 Question 1-4: What is the relationship between P and V? Is it proportional linear, inversely proportional, or
something else? Did this agree with your prediction? Question 1-5: Write down the relationship between the initial pressure and volume (Pi,Vi) and the final pressure
and volume (Pf,Vf) for an isothermal (constant-temperature) process. The relationship that you have been examining between P and V for a gas with the temperature and amount
of gas held constant is known as Boyle's law. If we additionally find the relationship between the Pressure and
Temperature with the volume of the gas held constant and the relationship between the volume and temperature
with the pressure held constant, we can deduce the ideal gas law.
Question 1-6: Is the relationships you found in the this activity consistent with the ideal gas law PV=constant .
T? Explain. Note that changing the temperature also affects the gas. We don’t have time to explore this quantitatively now,
but you can still feel it happen:
Activity 1-3: The Heated Syringe
You should have concluded from the last activity that the transfer of heat energy to a system can either
cause it to do work on its surroundings or increase its internal energy. What is the relationship between heat
energy transfer, changes in a system's internal energy, and the work done by the system? We picture U as the
"true" energy of the system. In the theory of thermodynamics, U is called a "state" variable, a quantity that tells
us some things we need to know to calculate useful things about a system, such as its temperature
Suppose that the piston of the syringe is clamped in place while the syringe is immersed in hot water. The
piston can't move, so no work can be done. However, since the water is initially at a higher temperature than the
gas in the syringe, we expect that heat energy is transferred from the water to the gas. This causes the
temperature of the gas to increase and the temperature of the water to decrease. The heat energy transfer can be
calculated using the equation Q= cm T, where c is the specific heat and T is the temperature change of the
water.
Assuming that the system is insulated so that no heat energy can be transferred to the surroundings, the
transferred heat energy Q must equal the increase in internal energy of the gas. This is based on a belief that
energy is conserved in the interaction between the hot water and the gas.
Suppose instead that we release the piston and allow the gas to do work as it expands against the piston. We
could calculate the amount of work W the expanding gas did by evaluating W = P V for the whole process.
Where did the energy to do this work come from? The only possible source is the internal energy of the gas,
which must have decreased by an amount W. The total change in the internal energy of the air trapped in the
syringe must be given by
U=Q-W
This relationship between transferred heat energy, work done on the surroundings, and the change in internal
energy is believed to hold for any system not just a syringe filled with gas. It is known as the first law of
thermodynamics.
The first law of thermodynamics has been developed by physicists based on a set of very powerful inferences
about forms of energy and their transformations. We ask you to try to accept it on faith. The concepts of work,
heat energy transfer, and internal energy are subtle and complex. For example, work is not simply the motion of
p.4 6/4/2013 the center of mass of a rigid object or the movement of a person in the context of the first law. Instead, we have
to learn to draw system boundaries and total the mechanical work done by the system inside a boundary on its
surroundings outside the boundary.
The first law of thermodynamics is a very general statement of conservation of energy for thermal systems.
It is not easy to verify in an introductory physics laboratory, and it is not derivable from Newton's laws. Instead,
it is an independent assertion about the nature of the physical world.
There are many ways to achieve the same internal energy change U. To achieve a small change in the
internal energy of gas in a syringe, you could transfer a large amount of heat energy to it and then allow the gas
to do work on its surroundings. Alternatively, you could transfer a small amount of heat energy to the gas and
not let it do any work at all. The change in internal energy, U could be the same in both processes. U
depends only on Q - W and not on Q or W alone.
Question 1-9: Can you think of any situations where W is negligible and U =Q? (Hint: Is it necessary to do
work on a cup of hot coffee to cool it? Can you think of similar situations?) Question 1-10: How could you arrange a situation where Q is negligible and in which U =-W? Such
situations have a special name in thermodynamics. They are called adiabatic processes. (Adiabatic means with
no heat energy transferred into or out of the system.) Investigation 2: Speed of Sound in the Air
1. You recall that we can also measure the speed of a wave – or anything else moving uniformly – by:
d=vt
where d is the distance traveled in a time t. Sound travels quickly, but with a good computer program, we
can measure the small time required for sound to move a significant distance.
With care (you remember The Three Stooges trying to carry long boards? Let’s not look like that here!)
place a 3.0 m long piece of sewer pipe across your lab table and your neighbor’s. (Lab groups at stations 5
and 6, place yours across the room on a couple of chairs.)
Slip a plastic pipe cap over the end away from you to reflect sound waves back.
2. Open the file called “Speed of Sound.aup” from the “Sound Lab” folder on your computer desktop. Choose
Record Sound.
Hold the microphone from your computer at the very edge of the pipe and facing into it. Hold your hand,
ready to snap your fingers, just behind the microphone. Or, hold a small hardback book in that position,
ready to smack it closed.
The microphone will receive the sound pulse directly from your finger-snap or book-slam, and an instant
later it will receive the fainter echo of that sound from the far end of the tube. Since we are making all time
measurements relative to the microphone, we don’t need to know the distance to your hand or book.
3. Be ready to click the round Record button, have your lab partner make the snap, then click the square Stop
button. You have now grabbed the entire event, and much more.
Then click View and Fit Vertically to adjust the amplitude to fit. Click and drag from just to the left of the
big peak (which includes the snap and the echo) all the way off to the left. Then press the Delete key to zap
p.5 6/4/2013 out that unwanted section. Click View and Zoom In (or click the magnifying glass) to look more and more
closely at that very beginning. Again, click and drag from the very peak of the snap to the left and press
Delete. Repeat until you feel comfortable that the peak is at time zero.
Zoom Out a bit to locate the next bunch of vertical peaks, which is the echo we are looking for. Click the
cursor on that second bunch and Zoom back In until you can confidently estimate the time, off the scale
above the wave, at which that wave arrived. (It should be around 0.016 to 0.018 sec.) That’s the time for
the sound wave to travel down the tube and back!
4. Now that you have that time, divide it into the distance the sound traveled. (Remember, the distance the
sound traveled is not the length of the pipe!)
5. Repeat the measurement twice more, record the values in the table below, find the average speed, and
round it to the nearest whole number.
Table 2-1.
Distance sound
traveled, d (m) Time for sound to
travel, t (s) Speed of sound,
v (m/s) Average Question 2-1. Check with your lab instructor to find the temperature in the room, T, in degrees Celsius.
Recalling that the speed of sound in air is given by
v = 331 m/s + (0.6 m/soC)T
What is the expected value of the speed of sound? Investigation 3: Waves on a string
In this investigation, you will try to oscillate the string at different frequencies. You will find that only a few
frequencies lead to waves that are large enough so that you see the wave clearly. You will see parts of the string
are nearly stationary (“nodes”: see figure 3) while other parts move strongly around equilibrium (the biggest
motion is at the “anti-nodes.”)
For a string, the velocity of the wave depends almost entirely on properties of the string (material and tension),
not on the frequency. This means that every frequency corresponds to a particular wavelength. Only some
wavelengths can fit “properly” on a string. You will find that the “proper” wavelengths depend only on how
you hold the string. The corresponding frequency is called a “resonance” frequency, because energy can build
up at these frequencies until there is enough motion for you to see.
Question 3-1: Draw a still image of a wave below, marking the wavelength. Also mark possible nodes (where
the wave doesn’t move). p.6 6/4/2013 Question 3-2: How is the distance between nodes related to the wavelength? Prediction 3-1: If you fix a string on two sides, draw what the longest “standing wave” could look like. What
is the wavelength for this wave, compared to the length of the string? Equipment:
Elastic String
Oscillator / Mechanical Vibrator
Vertical stand with horizontal posts
Meter stick
Activity 3-1: Both ends fixed
1. The oscillator has rubber feet on its bottom and also on one side. Lay the
oscillator on its side, on the rubber feet and align it so that the small
plastic fork holds the string but does not displace it. A slight forward
displacement will help keep the string in the fork when oscillating.
2. Check that the elastic string is attached to the posts on the vertical stand
by the loops that are tied on each end. The posts should be 1 meter apart,
if not adjust the clamps so they are, the lower post should be between the
table and the string vibrator, as figure 4.
3. Measure the length of the string between the two attach-points.
L=abcdefghidjck
4. Turn the oscillator on and set it to the lowers frequency setting. The
amplitude knob should only be set a quarter turn or so from the lowest
setting, it doesn’t take much movement. Slowly sweep frequency of
oscillator. You will find that only a few frequencies have a large enough
Figure 4. General layout of
amplitude that you see the wave clearly. Measure the distance between
equipment for vibrating string.
nodes (points that don’t move) for the largest wavelength you can find,
and write down this distance and the frequency in the table below, as well as in the experimental file. Find
at least 3 other frequencies with large amplitude waves, and fill out Table 3-1.
Table 3.1 Two fixed ends.
Longest
wavelength 2 3 Frequency
Distance between nodes
Wavelength
p.7 6/4/2013 4 Question 3-3: Did your longest wave fit your prediction 3-1?
Question 3-4: Can you find a relation between this “resonant” wavelength and the other ones that you found?
What about the frequencies? 5. Now take a wave with at least 2 nodes, and lightly pinch the string, first at a node and then at an antinode.
Question 3-5? What difference did you see? Did pinching the string at the node stop the wave? At the
antinode? Prediction 3-2. Now consider a string with one free end. A free end is always at a peak or valley, since that is
the only way forces can balance at the end of the string without something holding the other side. Draw the
longest resonant wavelength that will fit properly on this string. Comment: The velocity on the string depends on the tension in the string. To keep an end of the string free to
move while keeping the string under tension requires that the “free end” slide on a post holding it in tension, but
without any tension. Note that if there is any friction between the post and the string, the string isn’t “free. It’s
not easy to keep the friction low enough with simple equipment, but it is very easy using the computer to
simulate the action. In the next activity we are going to use such a simulation.
Activity 3-2: Compare: both ends fixed and one free end using computer simulation.
One Free end.
6. Open the simulation by opening the stlwaves.htm file in the Sound Lab folder on the desktop. This
simulation is also available on the internet at http://www.walter-fendt.de/ph14e/stlwaves.htm
7. Choose the length of the string (1 m). Notice that the author of this simulation chose the wave speed of
343.5 m/s.
8. Choose “both sides closed”.
9. For now, focus your attention on the first graph (the middle picture.) Find the lowest wavelength. Write
down the distance between nodes, the wavelength, and the frequency in Table 3-2.
10. Now choose “one side open”. Write down the distance between nodes, the wavelength, and the frequency
in Table 3-2, including the longest wavelength one (called the “fundamental” for a sound wave in music.)
You can find those with shorter wavelengths (higher frequency) by pressing “higher.”
Table 3-2. Compare: One free end and both ends fixed
Longest
wavelength 2 ends
fixed 2 3 Frequency
Distance
between nodes
p.8 6/4/2013 4 Wavelength
1 end
fixed, one
end free Frequency
Distance
between nodes
Wavelength Question 3-6. Did your longest wave with one free end and one fixed end fit your prediction 3-2?
Question 3-7. Can you find a relation between this “resonant” wavelength and the other ones that you found?
What about the frequencies? Comment: The resonance wavelengths for any wave depends only on the conditions at the ends of the waves
(boundary conditions: here, one or two fixed ends.) We can find these by just drawing the waves, fitting them in
the space, and realizing that any fixed end has to be a node, while a totally free end has to be an anti-node.
Once we figure out the resonance wavelengths, we can figure out the resonance frequencies, as long as
we know the relation between wavelength and frequency (by knowing the speed of the wave, for example.)
These ideas hold true not just for waves on a string, where we can visualize the string moving up and down, but
also for sound and light waves, where it is harder to visualize what is moving. We’ll see how they work for
sound in Investigation 4. INVESTIGATION 4: Sound waves in a tube
The computer simulation you just explored was in fact for sound in a tube. The wave speed was taken to be the
speed of sound at 20°C. The graph you were looking at was for the motion of particles within that tube: this
motion is back and forth along the tube (the direction of the wave), instead of up and down (perpendicular to the
wave direction) as on a string. These two types of waves are called “longitudinal” and “transverse”
respectively. You can get an idea of the “longitudinal” motion of sound from the picture above the graphs.
Note that the picture is very schematic, and doesn’t show what happens to air that was originally outside the
tube.
Note that at an open end, the air is free to move back and forth as it will (but with the same pressure as
the outside air), but at a closed end, the air must be stationary.
Prediction 4-1: What standing wave pattern (displacement of the air) do you expect for the various situations
for each of the tubes in each of the configurations given in Table 4-1 (sketch them in the spaces provided in the
table)?
Prediction 4-2: You haven’t measured the lengths of the tubes use in this activity yet, so use the letter L to
represent...

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