In-class group activity 4

Use an on-line simulation from the University of Colorado PhET group to become more familiar with Fourier analysis. 
 Link to the simulation: http://phet.colorado.edu/en/simulation/fourier.  Click "Run Now".

Open a Microsoft Word document to keep a log of your results and conclusions.   

Click the Discrete tab. 

(a)  Adjust the controls on the “Amplitudes” graph. 

• How does changing the “Amplitudes” graph change the “Harmonics” and “Sum” graph? 
  Explain how these three graphs are related.
  (Checking the “autoscale” box next to the “Sum” graph may make it easier to see what’s going on.)

(b)  Hit the “Reset” button so that there is only one sine wave shown.

• What is the definition of wavelength? 
  Use the horizontal zoom controls next to the “Harmonics” graph so that more than one period is displayed on the graph. 
  Check the “Wavelength Tool” box and use the tool that appears to measure from peak to peak, from trough to trough, and then from some arbitrary point in the wave to the same arbitrary point on cycle farther.  Is this consistent with your definition of wavelength?

(c)  Adjust the amplitudes to show more than one sine wave, and use the pull-down menu for the wavelength tool to compare the wavelengths of different sine waves.

• In general, does amplitude depend on wavelength?  Does changing the amplitude of a wave change its wavelength?
  What happens when you switch from showing “sines” to “cosines”?

(d)  Switch from a function of space to a function of time. 

• What changes? 
  What doesn’t change? 
  Explain why you can’t use the Period Tool in “space” mode or the Wavelength Tool in “time” mode.

(e)  Explore the different options in the “Select Function” pull-down menu. 

• For each function, try increasing and decreasing the number of harmonics.  What effect does this have and why? 
  What would happen if you had many more than 11 harmonics?  Test your prediction by checking the box labeled, “Show function with infinite number of harmonics.”

(f)  Select a triangle wave using sine functions. Look at the amplitudes of the different harmonics.

• Why are all the even harmonics zero?  (What happens if you change this?)
  Why is the third harmonic negative?  (What happens if you change this?)
  What happens if you switch from showing sines to cosines?