Phase Representation by Color in Complex Waves

We now take the linear dispersion, time dependent function from Section 2d and look at its behavior at the origin.  The applet on the left is a phasor plot of the amplitude at the origin.  The projection along the x - axis is the amplitude at an instant in time.  The angle the arrow makes with the positive horizontal axis is the phase angle.

Student Exercises:

1. Write the time dependent equation for the point at the origin divided by 9.  What will be the range of the resultant function?
2. At t = 0, calculate the value of the function found in Exercise 1?  To what phase angle would this correspond?
3. At t = 0.26, calculate the value of the function found in Exercise 1?  To what phase angle would this correspond?  Move to this time in the applet and check your answer. 
4. At t = 0.52, calculate the value of the function found in Exercise 1?  To what phase angle would this correspond?  Move to this time in the applet and check your answer. 

The value of the function at each point along the x-axis, not just the origin, can be described by a phase angle.  Another way to visualize the behavior of the above wave then is to use color to describe the phase of the wave at any point much like what we did in Section 1b.  Such a description would be a wave of constant amplitude with colors varying in time and space.  The wave we have here is a real traveling wave.  The wave in Section 1b was a complex wave of constant amplitude.  In Section 3 we will combine what we have done in Sections 1 & 2 to examine the time development of a localized complex wave.

 Return to initial page of Section 2d.  

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