Waves
Names:____________________
____________________
Introduction:
Waves are everywhere in nature – from the water in your bathtub to the light that is
reflecting off of this paper, allowing you to read these words. In this lab we will examine
different types of waves.
Part 1: Slinky® Waves
For this part of the lab you will work in teams of four students.
A. Transverse Waves: On your lab table you will find a large Slinky toy, a roll of
masking tape, a stop watch, and a meter stick. Gather these together and go out into the
hall. The class should spread out so each group has about five meters of space in which
to work.
Stretch your Slinky out on the floor. You should stretch it to the point it is straight, but not
taut. Measure the length of the Slinky while it is held it in place. You may use the tape to
mark positions on the floor. Note: each floor tile is 30.5 cm.
Length of stretched Slinky: _______________m.
A single waveform is called a pulse. While holding one end of the Slinky in place, wiggle
the other end back and forth to generate a series of pulses. This will generate a
transverse traveling wave. A traveling wave is one in which the waveform moves
through the medium. In a transverse pulse or wave the medium in which the wave is
traveling oscillates perpendicularly to the direction of the pulse or wave’s motion. Sketch
a ‘snapshot’ of the wave as if moves up and down the Slinky.
On your picture label the wavelength of the wave. The amplitude of a wave is its
maximum displacement from the equilibrium position. Label the amplitude of your wave
on your picture.
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While holding one end of the Slinky in place, wiggle the other end side to side once.
This will generate a single transverse pulse. Sketch the shape of the pulse just before
and just after it reflects off the far end of the Slinky.
What has changed about its shape? Did the size of the pulse change upon reflection?
B. Speed of the pulse: Using the known length of the stretched Slinky and the
stopwatch, calculate the speed of the pulse as it travels up and down the Slinky once.
The pulse’s amplitude should be about one floor tile width. Repeat your measurement
three times and find the average.
Amplitude of pulse: One floor tile
Trial
Time for pulse to return to
sender (seconds)
1
2
3
Speed
(meters/second)
Length of stretched Slinky: _______________m
Average speed of pulse:____________m/s.
Generate a pulse with a larger amplitude (two floor tile width). Measure the speed of this
pulse.
Amplitude of pulse: Two floor tiles
Trial
Time for pulse to return to
sender (seconds)
1
2
3
Speed
(meters/second)
Length of stretched Slinky: _______________m.
Average speed of pulse:____________m/s.
Does the speed of the pulse depend on the amplitude of the pulse? _______________.
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Stretch the Slinky a little further. About 50 cm to 1 m should be enough. Do not overstretch the Slinky. Measure the speed of the pulse with an amplitude of one floor tile
again.
Amplitude of pulse: One floor tile
Trial
Time for pulse to return to
sender (seconds)
1
2
3
Speed
(meters/second)
Length of additionally stretched Slinky: _______________m.
Average speed of pulse:____________m/s.
What was the effect of stretching the Slinky on the speed of the pulse? What properties
of the Slinky changed when you stretched the Slinky that might have caused the speed
to change?
C. Longitudinal Waves: In longitudinal waves the medium in which the wave is
traveling oscillates in the direction of the wave’s motion. While one end of the Slinky is
held still, pull the other end in and out and generate a series of longitudinal pulses. This
is longitudinal traveling wave. Sketch a ‘snapshot’ of the wave as if moves up and down
the Slinky.
On your picture label the wavelength of the wave. In a transverse wave the wavelength
is defined as the distance between adjacent crests. Complete the following sentence:
The wavelength in a longitudinal wave is the distance
between____________________________.
How would you define the amplitude of this kind of wave?
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Return the Slinky to its original stretched length. Again with one end of the Slinky held in
place, gather about three tile lengths of the Slinky together and then release the
gathered coils while still holding onto the end of the Slinky. Measure the speed of this
pulse.
Longitudinal pulse: Amplitude three tile lengths
Trial
Time for pulse to return to
sender (seconds)
1
2
3
Speed
(meters/second)
Length of stretched Slinky: _______________m.
Average speed of pulse: ____________m/s.
Does the longitudinal pulse travel at the same speed as the transverse pulse? _______.
D. Standing Waves: Standing waves are waves in which the position of the waveform
does not change with time. The positions where the Slinky is displaced the most are
called antinodes. The positions where the Slinky is not displaced are called nodes. So in
a standing wave the nodes and antinodes do not move.
The standing wave pattern with one antinode in the middle of the Slinky occurs at what
is called the fundamental or first harmonic frequency, and is called the first harmonic
mode. Practice wiggling one end of the Slinky until you can generate a standing wave
with one antinode. You may need to stretch the Slinky more in order to find the first
harmonic. Then increase the frequency until you can produce the second harmonic
mode (two antinodes) and third harmonic mode (three antinodes). Can you get to the
fourth harmonic?
Working with another group, stretch two Slinkys side-by-side leaving enough space in
between them so that they can both wiggle back and forth without touching. Gather
some of one end of one of the Slinkys so that it is the same length as the other Slinky,
but under more tension. On one Slinky set up a standing wave. On the other Slinky
attempt to match the frequency of the first Slinky, so that both Slinkys are being wiggled
at the same rate. Does this result in a standing wave on the second Slinky? Why or why
not?
Gather your supplies back together and return to the laboratory. Make sure to remove
any tape from the floor. You will do the next part of the lab in pairs.
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Part 2: Vibrating String
The speed, v, in meters per second, with which a transverse wave pulse travels along a
flexible string is given by the equation
v
F

(1)
,
where F is the tension in the string, in newtons, and μ is the mass per unit length of the
string, in kilograms per meter. If a series of wave pulses of frequency f travels along this
string, the wavelength, frequency, and velocity will be related by
(2)
v = f·λ.
But it is hard to measure the velocity of a wave in a string directly. It is also difficult to
measure the wavelength of a traveling wave. It is possible, however, to measure the
wavelength and frequency in a standing wave. Eliminating v between Equations (1) and
(2), we have
f 
(F /  )1 / 2

.
(3)
The measurement of F and μ are relatively straightforward. To measure λ we relate the
number of antinodes and the length of the string to the wavelength. Figure 1 shows a
string vibrating at a frequency that generates a standing wave. The distance between
two successive nodes (or antinodes) is just equal to one-half of the wavelength.
Therefore, when standing waves are produced, it is an easy matter to pick out the
positions of the nodes and antinodes and thus measure the wavelength.
Figure 1 – Standing Waves
For a given frequency and string length L, appropriate changes in the tension will set up
different standing wave patterns on the string. See Table 1.
From the last column in Table 1 the following equation relating λ, L and n can be found.

2
L.
n
(4)
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By substituting Equation (4) in Equation (3) one obtains
F

1
 4  L2    f
2
n
2

(5)
Equation (5) provides a simple relationship between f, F, and n that can be used to
deduce the value of f from measurements of F for different values of n, and known
values of L and μ. Note that Equation (5) is independent of λ.
Table 1
In this laboratory exercise the quantity between parentheses in Equation (5) will remain
constant throughout the experiment, with L and μ measured, and f being the unknown.
We will adjust the tension on the string in order to form standing wave patterns. Patterns
with a large number of antinodes are produced by reducing the tension, as Equation (5)
indicates. The pattern with two antinodes at the middle of Table 1 required more tension
than that with three antinodes, and so on.
In order to calculate μ, the linear density of the string, first measure the mass and the
length of a loose piece of string provided by your lab instructor. This string is similar to
that attached to the vibrator.
Mass of loose string: __________kg.
Length of loose string: ____________m.
μ for string: ___________kg/m.
With the experimental set up arranged as shown in Figure 2, plug in the vibrator power
cord and adjust the screw until the spring scale reads 20 N, which is its maximum
capacity.
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Measure the length of the string between the vibrator and pulley (L). Make sure you are
only measuring the part of the string that is free to vibrate. L: _________m.
Calculate 4·L2 ·μ: _____________kg·m
Slowly reduce the tension in the string by turning the screw in the opposite direction. At
some lower tension a standing wave pattern will form on the string. (It will have a integer
number of antinodes.) Adjust the screw up and down until the vertical displacement of
the string at the antinodes is maximized.
Figure 2. An electrically string vibrator of constant frequency generates standing waves on a
string at appropriate tensions.
Fill in the table below with the value of n-2 and the value of F read on the spring scale.
Repeat the procedure described above for five more standing wave patterns.
n
number of antinodes
n-2
1
2
3
4
5
6
7
F (N)
tension on string
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Make a graph of F vs. n-2. Perform a linear fit to your data. Since the slope of the line =
4·L2 ·μ·f 2 find f. Show your work below.
f (calculated) : __________Hz.
At this point show your instructor your measured value of the vibrator’s frequency, and
obtain the factory specification for the frequency. Compare these values.
f (factory): ___________Hz.
Percent difference: __________%
Is your calculated value of f in good agreement with the factory specification? If not, what
would you do in order to improve your results?
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