Waves on String

1. Go to the “Waves on String” simulation on Moodle.  Once you have the simulation running play
around with it for a while to familiarize yourself with the interface.  Once you are comfortable set the
simulation up as follows.  For now we are not interested in reflections from the end so select the “No
end” button.  We are also not interested in damping of waves so set the “Damping” slider to zero.
Click on “Rulers” and “Timer” so that you have rulers and a stopwatch available.  Set the “Tension”
slider to “low”.  Make sure that the “Manual” button is pressed (one end of the string should be held in
a wrench that you can move manually).
(a) Wiggle the wrench up and back down to its original position fairly quickly.  Let the
resulting wave travel a short distance (say 20 or 30 cm) and then slowly wiggle the wrench
up the same distance and back to its original position.  You might want to go through this
whole process a few times to make sure you see what is going on.  [3 marks]
i. Do the waves travel at different speeds (e.g. does the first wave leave the second one
behind or do they travel along with the distance between them staying the same)?
ii. Compare the wavelength of the two waves.
iii. Compare the particle speed that the pieces of the string have as each wave passes by.
(b) Now click the “Oscillate” button (the wrench will be replaced with a device that drives one
end of the string with a steady oscillation).  Leave the tension on “low” and set the
frequency of the driver to “5”.  Now use the timer to time several oscillations of the driver
and determine what the frequency of the driver is in oscillations/s. [1 mark]
(c) Pause the simulation and use the horizontal ruler to measure the wavelength of the waves.
Make peak-to-peak measurements, trough-to-trough and “crossing-to-crossing”
measurements to verify that they are the same. [2 marks]
(d) Pause the simulation when the driver is at a maximum. Set the ruler with the zero end at a
peak in the waves.  Run the simulation for one full oscillation of the driver (use the step
button if necessary to get as close to exactly one full oscillation as you can).  How far has
the peak gone that was at the zero end of the ruler?  How far does a wave travel in one
full period? [2 marks]
(e) From your knowledge of the wavelength, and how long it takes for a wave to travel one full
wavelength, determine the speed of the wave. [1 mark]
(f) Measure frequencies and wavelengths of these waves to fill in the table below: [6 marks]
Frequency setting Tension setting Measured frequency
(Hz)
Measured wavelength
(cm)
Wave speed
“5” “low”
“10” “low”
“5” halfway between “low
and “high”
“10” halfway between “low
and “high”
(g) How does increasing the frequency change the behaviour and appearance of the waves?
How does increasing the tension change the behaviour and appearance of the waves? [4 marks]
PHYS 1201 Assignment #3: Waves Due: Mon., Feb 2
nd
, 2015
2. Cables that are used to support structures sometimes need to be tested in place to ensure that
they are in good shape and at the proper tension. One way to do this is to send waves through them and
examine the speed and other properties of the waves.
An oscillator is attached to one end of a cable which produces transverse waves. A detector is
placed 10 m down the cable which is able to sense motion of the cable. If the cable is at the correct
tension and in good shape then the wave speed on the cable should be 2.54 x 10
3
m/s.
(a) The oscillator vibrates with a frequency of 282 Hz.  What is the period of the oscillation? Assuming
that the cable is in good shape and at the correct tension, what should the wavelength be? [2 marks]
(b) On the electronic readout of the test equipment we see that the wire is oscillating with an amplitude
of 3.00 mm and that at t = 0 the end attached to the oscillator has at the top. Using the oscillator as the
origin of our coordinate system, write the function that describes this wave. [3 marks]
(c) Draw a snapshot graph of the displacement at t = 0, D(x, t = 0). Be sure to label your axes with the
appropriate units.[4 marks]
(d) At t = 0 what should the phase of the wave be at the location of the detector, 10 m away from the
oscillator? (Recall: the phase is the ‘argument’ inside the cosine) [2 marks]
(e) Draw the history graph for x = 10m.  Show at least two cycles of the motion.  [Note: this should be
easy, since you have just calculated the phase at (x=10m, t=0s), and you know the period from a)] [3
marks]
(f) The electronic readout shows that at t = 0 the displacement of the wire at x = 10 m is 0.15 mm. Does
this match the expected displacement that would be seen if the cable was in good shape and under
correct tension? [2 marks]
3.The figure shows a snapshot graph at t = 8 s of a wave
travelling at 0.5 m/s to the right.
(a) Redraw the snapshot graph but at t = 0 s so you are drawing
D(x, t = 0). [2 marks]
(b) Draw the history graph, D(x = 3, t), for the point at x = 3 m.
Be sure to show your work, especially how you found the times
when the “leading edge” and “trailing edge” of the wave passed through x = 3m. [3 marks]
(c) Now suppose that the wave were travelling at 2 m/s to the left instead but that its snapshot graph at
t = 8 s was otherwise the same. Draw the history graph, D(x = 3, t) of the point at x = 3 m for this case.
[3 marks]

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