Mechanical Waves
A wave pulse is a disturbance that moves through a medium. A
periodic wave is a periodic
disturbance that moves through a medium. The medium itself goes nowhere.
The individual atoms and molecules in the medium oscillate about their
equilibrium position, but their average position does not change. If the
displacement of the individual atoms or molecules is perpendicular to the
direction the wave is traveling, the wave is called a transverse wave. If the displacement is parallel to the
direction of travel the wave is called a longitudinal wave or a
compression wave.
Waves can transport energy and information. Examples of mechanical
waves are water waves, sound waves, and seismic waves. All waves are described
mathematically in terms of a wave function, and reflection,
refraction and diffraction and
interference a characteristic behaviors of all types of waves.
In this session you will study wave motion in one dimension only, to learn
about several of these characteristic behaviors. You will study the motion of
waves on a string.
Equipment needed:
 electric string vibrator
 pulley
 base and support rods and clamps
 mass hanger and mass set
 level
 meter stick
Open a Microsoft Word document to keep a log of your
experimental procedures, results and discussions. Address the points highlighted in blue. Answer all
questions.
Exploration
Use an online simulation from the University of Colorado PhET
group to explore the behavior of waves on a string.
Link to the simulation:
http://phet.colorado.edu/en/simulation/waveonastring
(a) Explore the interface. Try the different controls.
(b) Investigate the behavior of a wave pulse.
 Start with the following settings:
 Pulse
 No End
 Amplitude: 0.5 cm
 Pulse Width: 0.5 s
 Damping: none
 Tension: high
 Ruler and timer: checked
 Observe this pulse and measure its speed in cm/s.
(You can start and stop the pulse and use slow motion.)
 Vary (one at a time) amplitude, pulse width, damping, and tension, and
describe what happens.
 Return to the original pulse but change the end to a loose end and the
to a fixed end and describe what happens.
(c) Investigate the behavior of a traveling wave.
 Start with the following settings:
 Oscillate
 No End
 Amplitude: 0.5 cm
 Frequency: 1.5 Hz
 Damping: none
 Tension: high
 Ruler and timer: checked
 Observe this wave (wave 1) and make measurements. Enter your measurements into the table.
 Measure the amplitude of the wave in cm.
 Measure the wavelength in cm.
 Measure the period in s.
 Find the speed of the wave in cm/s.

wave 1 
wave 2 
wave 3 
wave 4 
wave 5 
amplitude A 





wavelength λ 





period T 





frequency f 





speed v 





 Move the amplitude slider to 0.25 cm (wave 2)
and then to 0.75 cm (wave 3).
Make new measurements. Describe what changes.
 With the amplitude slider at 0.5 cm, move the frequency slider to 1 Hz (wave 4) and then to
2 Hz (wave 5).
Make new measurements. Describe what
changes.
 Discuss the relationships between wavelength and frequency, period and
frequency, amplitude and frequency and speed and frequency.
 Can you change the speed of the wave? What can you do to produce a
wave that moves with approximately 1/4 the speed of wave 1.
 Describe what happens when you include damping.
(d) Investigate the behavior of a standing wave.
 Start with the following settings:
 Oscillate
 No End
 Amplitude: 0.5 cm
 Frequency: 1.5 Hz
 Damping: one notch
 Tension: high
 Ruler and timer: checked
 Describe the wave. What is its maximum amplitude in cm? Does
this maximum amplitude change when you change the frequency slider?
 Change the end to a fixed end, the frequency to zero, and click the
restart button.
 Slowly increase the frequency.
Wait several seconds to see what happens to the maximum displacement
from equilibrium of the wave for each frequency setting.
 For which frequencies between zero and 1.5 Hz is the maximum displacement from equilibrium
largest (larger than that of the traveling wave)? In other
words, for which frequencies do you hit resonance? What happens if you set
the damping to zero at those frequencies?
 What can you say about the wavelengths associated with those frequencies?
Experiment
Standing waves of many different wavelengths can be produced on a
string with two fixed ends, as long as an integral number of half wavelengths
fit into the length of the string. For a standing wave on a string of length L
with two fixed ends
L = n(λ/2), n = 1,2,3,... .
 Fundamental: L = λ/2, n = 1, 1/2 wavelength fits into the length of the string.
 Second harmonic: L = λ n = 2, one wavelength fits into the length of the string.
 Third harmonic: L = 3λ/2, n = 3, 3/2 wavelengths fit into the length of the string.
For a string the speed of the waves is a function of the mass per unit length
μ = m/L of the string and the tension F in the string.
v = √(F/μ).
In this lab, waves on a string with two fixed ends will be generated by a
string vibrator. The waves will all have a frequency of 120 Hz. Their wavelength
is given by λ = v/f. Since the frequency is
fixed, the wavelength of the waves can only be changed by changing the speed of
the waves. You will adjust the
tension in the string until 1, 2, or 3 half wavelength of a wave with f = 120 Hz
fit into the length of the string. Then 120 Hz is a natural frequency of the
string and the vibrator drives the string into resonance. The amplitude
increases and the standing waves can easily be observed.
Summary:
Given: f = 120 Hz.
Measure: tension F, for λ = L/2, L, 2L/3
Calculate: the mass per unit length μ of the string,
using v = λf, μ = F/v^{2}.
Procedure:
 Mount the vibrator on a rod which is fixed to the table with a clamp.
Mount the pulley onto another rod fixed to the table with a clamp. Pass a
string from the vibrator over the pulley and attach a mass hanger. Make
sure the string is level. You now have a string with two fixed ends.
 The amplitude of the vibrator arm is so small compared to the
amplitude of the string at resonance, that the vibrator is very close to a node.
 Open an Excel spreadsheet and paste the table below into the spreadsheet.

n 
measured L (m) 
λ_{n} = 2L/n (m)_{ } 
speed v_{n} = fλ_{n}(m/s) 
hanging mass at resonance (kg) 
measured F = mg (N) 
Fundamental: (n = 1) 
1 





Second harmonic: (n = 2) 
2 





Third Harmonic: (n = 3) 
3 





 Let the length of the string from the vibrator to the top of the
pulley be somewhere between 0.8 m and 1.2 m. Enter the length L into
the appropriate cells of the spreadsheet.
 For your chosen length L use the spreadsheet to calculate the wavelength λ_{n}
= 2L/n and then the speed v_{n}= fλ_{n} = 2fL/n of the fundamental and second and third
harmonic for f = 120 Hz.
 Turn on the vibrator. Try to produce the fundamental standing wave on the string.
Adjust the amount of mass hanging from the string until the string is driven into
resonance. Enter the measured value for the hanging mass. Calculate the measured force F =
mg. (g = 9.8 m/s^{2})
 Repeat for the second and third harmonic and fill in the table.
Data Analysis:
Calculate the mass per unit length μ of the string using μ
= F/v^{2}. Average the values obtained from your three measurements
and estimate the uncertainty in this average value.
Discuss:
 Were you able to clearly identify the resonances?
 How do your values of μ obtained from the three measurements compare? In your opinion, are they equal within
experimental uncertainties. If not, what do you think can explain the differences?
Convert your log into a session report, certify with you signature that
you have actively participated, and hand it to your instructor.