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.
- 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).
- 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 |
- 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 |
- What is the wavelength (distance between peaks) of the wave?
- 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)?
- What is the speed of the wave?
Exploration authored by Melissa Dancy and modified by Anne J. Cox.
