SCIE1010
Lab 6 Waves
Name __________________
3/28/2011
Experiment 6
W a ve s
INTRODUCTION
Waves are a means of propagating energy by particle disturbances. Most students are familiar with
water waves, sound waves, light waves, and waves in stretched strings like piano or guitar strings.
Particle disturbance means that the particle has been displaced from its equilibrium position by some
agent. Once displaced, the particle tends to return to its original position. In the process, a wave will
be propagated outward from the disturbance, transferring energy. The propagation of energy from the
disturbance is called wave motion.
Waves are classified as transverse or longitudinal. Transverse waves have the particle
displacement perpendicular to the motion of the wave. Longitudinal waves are those in which the
particle displacement is in the same direction that is parallel to the direction of the wave motion.
All waves have certain fundamental properties. A few of these properties are wave velocity,
wavelength, period, frequency, and amplitude. These are illustrated in Fig. 11.1 on the next page.
The wave velocity of the wave is the distance the wave travels per unit of time, and in this
experiment it is measured in centimeters per second. The wavelength is the distance between two
consecutive wave crests or wave troughs and is measured in centimeters or some other unit of length.
The period of a wave is the time required for one wavelength to pass any point along the direction of
travel. The frequency is the number of vibrations or cycles per unit time the particle disturbance is
taking place. Frequency, f, is usually measured in cycles per second, or Hertz. The period T is the
reciprocal of the frequency. You will recall that the reciprocal of a number is one divided by the
number. The relation here, therefore, would be written as
f 1
T
T 1
f
where T is the period in seconds and f is the frequency in cycles per second.
The relation among velocity, frequency, and wavelength is shown by the equation
vf
where _   wavelength
v = f
f  frequency
v  velocity
Page 1 of 11
SCIE1010
Lab 6 Waves
Name __________________
3/28/2011
Figure 11.1 Transverse Wave Properties.
LEARNING OBJECTIVES
After completing this experiment, you should be able to do the following:





Define the terms wave velocity, wavelength, frequency, period, and amplitude for a wave.
Differentiate between longitudinal and transverse waves.
Demonstrate the transfer of energy by wave motion.
Measure the wave velocity in a stretched rubber rope or hose.
Measure the wavelength of a sound wave.
APPARATUS
Metal can with plastic lid (large-sized coffee can with about 1 inch hole cut into the flat metal end),
candle, 2-m meter stick, rubber cord, timer, coiled spring, tuning forks (use frequencies high enough
to give two or three maximum and minimum points for air column in closed pipe), a 1,024 cps tuning
fork, rubber hammer, resonance apparatus, large water tray, cork stopper.
Page 2 of 11
SCIE1010
Lab 6 Waves
Name __________________
3/28/2011
Open flame from a candle can be dangerous. Do not leave
lighted candles unattended or reach across flame.
LABORATORY SECTION ________ PARTNER(S) ___________________________________________________________
PROCEDURE
1.
Assemble the metal can, meter stick, and candle as shown in Fig. 11.2. Determine if you are
able to extinguish the candle flame one meter (or less) from the can by lightly thumping the
plastic lid with a rubber hammer Explain your results.
2.
The velocity of a wave in a stretched string or rubber cord is given by the following:
v
F
m
L
where v = velocity
F= tension in cord measured in units of force
m/L = mass per unit length
Attach the rubber cord to one wall of the laboratory, and then apply tension to stretch the
cord across the room. Displace the cord as shown in Fig. 11.3. Observe the wave travel the
length of the cord, be reflected at the wall, and return to your hand. Note: Do not stretch the
hose too tight or the wave pulse will travel too fast for you to time accurately.
Figure 11.3
Page 3 of 11
SCIE1010
Lab 6 Waves
Name __________________
3/28/2011
With the timer determine the time (three trials) it takes a wave to travel the total distance (d).
Measures the distances traveled, and calculate the velocity of the wave using the average value
from your three time trials. Since the wave moves quite rapidly you may wish to measure the
time the wave pulse to travel back and forth between your hand and the wall several times
and then divide the total distance by the total time to find the wave velocity.
Remember the definition of velocity:
v
d
t
Repeat the experiment with increased tension in the cord.
Page 4 of 11
SCIE1010
Lab 6 Waves
Name __________________
3/28/2011
What effect does increasing the tension have on the wave velocity?
What type of wave is traveling in the cord? Explain your answer.
1. Stretch the coiled spring along the floor. Displace the spring at one end by compressing a few
coils and releasing. Observe the wave motion along the spring. Explain the type of wave
observed.
3.
Fill the large tray with water; then place it on the laboratory table. Place the cork stopper in
the water near one end of the long dimension of the tray, as shown in Fig. 11.4. Disturb the
water near the other end of the tray by dropping a coin flat into the water.
Figure 11.4
Observe the wave motion on the water and the movement of the cork. What type of wave are
you observing? Explain your answer.
5.
Page 5 of 11
SCIE1010
Lab 6 Waves
Name __________________
3/28/2011
In the introduction, wavelength was defined and illustrated. Fig. 11.5 illustrates the component sections
of one complete wavelength.
1
a
4

b
c
½λ
d
e
Figure 11.5
Note that minimum particle displacement occurs at positions a, c, and e. These points are
called nodes. Maximum displacement occurs at b and d which are referred to as antinodes. The
distance ab is one-fourth wavelength. Likewise the distances bc, cd, and de are one-fourth
wavelengths. Observe that one maximum and one minimum value occur in each quarter-wavelength.
Figure 11.6 illustrates the particle displacement along a quarter-wave tube containing a vibrating
column of air produced by a tuning fork. The air at the open end of the tube will vibrate at the
maximum value because at the open end the air is free to move. At the lower end of the tube,
minimum particle displacement will take place because the tube is closed and particle vibration is
restricted.
Page 6 of 11
SCIE1010
Lab 6 Waves
Name __________________
3/28/2011
Figure 11.6 Air column in a pipe opened at the top and closed at the bottom.
Maximum
vibration
(loud)
4
Minimum
(soft)
vibration
Air
Maximum
vibration
(loud)
Minimum (soft)
Vibration
12
L
2
Water
1
Using such a resonance apparatus, we can determine the wavelength of a sound wave. A
simple model of this apparatus is shown in Fig. 11.7.
The height h may be a quarter-wavelength or a whole-odd-number multiple of a quarterwavelength (2/4, 3214, 52/4, ...). In using the apparatus to determine the wavelength of sound, all
that is necessary is to adjust the length of the air column by adjusting the water level for the loudest
sound heard. Record the air-column length for this maximum loudness; then adjust the level again for
the next maximum loudness level. The distance between two maximums is one-half wavelength.
The velocity of sound in air in meters per second can be calculated from the following
equation:
v = 332 m/s+ (0.60 m/s)T
where v = velocity of sound in air
332 m/s = velocity of sound in air at 0° Celsius
T = temperature of air in degrees Celsius
Page 7 of 11
SCIE1010
Lab 6 Waves
Name __________________
3/28/2011
Using this information and the equation relating velocity, wavelength, and frequency,
=
calculate the theoretical value of one wavelength for the waves produced in the air column
by a 1024-cycles-per-second tuning fork.
Theoretical value of wavelength A= _________
h
Figure 11.7 Resonance apparatus.
Experimental Determination of Wavelength:
A: Strike the 1024-cps tuning fork with the rubber hammer. Place the vibrating fork at the top of the
air column and adjust the water level until the air column is vibrating at its maximum loudness.
You will be able to ascertain the maximum loudness by listening. Record the length of the air
column. Readjust the water level to the next maximum loudness position. Record the length of
the air column and calculate the value of a half-wavelength by subtracting these lengths.
Page 8 of 11
SCIE1010
Lab 6 Waves
Name __________________
3/28/2011
Experimental value of half-wavelength λ/2= ______________

Wavelength   2   , = ___________
2
frequency 
v

= _________________________
Percent difference between measured and theoretical wavelength
% difference =_________
B: Determine the wavelength and frequency of an unknown tuning fork using the resonance
apparatus.
 
Wavelength   2  = _________________
2
Frequency frequency 
v

=___________________
Ask the laboratory instructor for the correct value of unknown frequency, and determine the
percent error using the instructor's value as the accepted value.
f (given by instructor) = ____________
Percent error =______________
QUESTIONS
1.
Define wave motion, and give an example.
2.
Distinguish between longitudinal and transverse waves.
Page 9 of 11
SCIE1010
Lab 6 Waves
Name __________________
3/28/2011
3.
Define the velocity, wavelength, and frequency of a wave and give an example of each. Use
symbol notation in the definitions.
4.
State the relationship between velocity, wavelength, and frequency of a wave.
5.
Define the amplitude of a wave, and give an example.
6.
State the relationship between the frequency and the period of a wave.
Page 10 of 11
SCIE1010
Lab 6 Waves
Name __________________
3/28/2011
7.
How do your measurements in Procedure 2 predict the way that the velocity of a wave in a
rubber cord varies with the tension in the cord?
8.
Why is there a maximum vibration of the air molecules at the open end of a resonance tube?
9.
How does the velocity of sound in air vary with the air temperature?
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