In this laboratory you will study wave motion in one dimension only, to learn about several of their characteristic behaviors. You will explore the motion of waves on a string.
Open a Microsoft Word document to keep a log of your experimental procedures, results and discussions. This log will form the basis of your lab report. 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
Click "Run Now!" or
"Download"
(a) Explore the interface. Try the different controls and click "Help" to discover features you otherwise may miss.
(b) Investigate the behavior of a wave pulse.
Start with the following settings:
 
Observe this pulse and measure its speed in cm/s.  
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:
 
Observe this wave (wave 1).
Describe your observations.

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 25 (wave 2) and then to 75 (wave 3), and describe what changes.  
With the amplitude slider at 50, move the frequency slider to 25 (wave 4) and then to 75 (wave 5), and describe what changes.  
Paste your table into your log.  
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:
 
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
reset button.

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.
In this experiment waves on a string with two fixed ends will be generated by a string vibrator. The waves will have a frequency of 120 Hz. Their wavelength is given by λ = v/f. You will analyze video clips in which the string tension F is fixed and the length of the string is being varied. You will measure the length of the string when the string supports a standing wave such that 1, 2, or 3 half wavelength of a wave 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.
You will analyze three video clips, string_x.mp4, x = 1  3. To play a video clip or to step through it framebyframe click the "Begin" button. The "Video Analysis" web page will open.
The string is 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. The other node is the top of the pulley.
Step through the video clip string_1.mp4 frame by frame. You will see the vibrator drive the string into resonance when the length of the string becomes equal to exactly 1/2 wavelength of a standing wave. Locate the frame in which this happens and hold the clip at that frame.  
Choose to track the xcoordinate and calibrate x. Use the 0.2794 m long marker for the calibration.  
Click "Start Taking Data".  
Click on the node at the vibrator for your first data point. Then click "Step Down" once, to return to the same frame and click on the node on top of the pulley for your second data point. Find the distance between the two nodes L (the difference between the two x values).  
Open Excel and construct a spreadsheet as shown below. Enter
L, λ and the string tension F given in the
clip. For the fundamental λ = 2L.
 
Repeat the experiment using the video clips string_2.mp4 and string_3.mp4. These clips show the second and third harmonic, respectively. For the second harmonic λ = L and for the third harmonic λ = 2L/3.  
For waves on a string we have F = μv^{2}. This tension is provided by a hanging mass, F = mg. Calculate v and v^{2} and plot F versus v^{2}. Use Excel's regression function to find the slope of the best fitting straight line to this plot. This slope is equal to the mass per unit length of the string μ. The uncertainty in the slope equals the uncertainty in μ. 
Paste your spreadsheet and your plot into your log.
Answer the following questions:
What is the mass per unit length μ of the string in units of kg/m and what is the uncertainty in this value as determined from your measurements.  
Refer to the video clip string_1.mp4. How much hanging mass would be needed to produce a resonance of the fundamental standing wave, if the string had same length L but only half the linear density μ?  
Refer to the video clip string_1.mp4. How much hanging mass would be needed to produce a resonance of the fundamental standing wave, if the string had same linear density μ but twice the length L? 
Convert your log into a lab report. Make sure you have addressed all items in blue, and you are describing your procedures, results and conclusions in complete sentences
Save your Word document (your name_lab10.docx), go to Blackboard, Assignments, Lab 10, and attach your document.