Exploration 32.1: Representation of Plane Waves

Please wait for the animation to completely load.

Move the slider and observe the animation on the left-hand panel of your screen.  The animation shows the electric field in a region of space.  The arrows show the field-vector representation of the electric field.  The amplitude of the field is represented by the brightness of the arrows.  The slider allows you to move along the z axis.  Notice that the electric field is always uniform in the xy plane but varies along the z axis (position is given in meters and time is given in nanoseconds).  Restart. 

  1. Construct a graph that represents the electric field along the z axis at t = 0 ns.

Now view a representation of the electric field.  Click-drag inside the animation on the right to view the electric-field representation from different points of view.  This representation should closely match the graph you drew for (a).  Click on "play" to see a traveling wave.  The representation on the right is often used to show a field like that on the left.  Remember that the representation on the right is actually a graph of amplitude along the direction of propagation (z axis). 

  1. Keeping that in mind and looking at the graph on the right, rank the amplitude of the field at t = 0 ns for the following locations, from smallest to largest. 
Location x coordinate  y coordinate z coordinate
I 1 0 -1.5
II 1 1 -1.5
III 0 0 -1.5
IV 0 1 -1.0
V 1 1 -0.5
  1. Now, push "play" to see the traveling wave.  At position z = -0.5 m, rank the amplitude of the field at the following times (approximately), from smallest to largest.
Time (ns) x coordinate  y coordinate z coordinate
t = 0 1 1 -0.5
t = 1.7 1 1 -0.5
t = 3.3 1 1 -0.5
t = 5.0 1 1 -0.5
t = 6.7 1 1 -0.5
  1. What is the wavelength (distance between peaks) of the wave? 
  2. What is the frequency of the wave (the period T = 1/f is the time it takes for the wave to repeat itself at a given location)? 
  3. What is the speed of the wave?

 

 

Exploration authored by Melissa Dancy and modified by Anne J. Cox.
© 2004 by Prentice-Hall, Inc. A Pearson Company