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# Exploration 32.1: Representation of Plane Waves

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.

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