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Illustration 18.1: Representations of Two-Dimensional Waves
Please wait for the animation to completely load.
The animation will run for thirty seconds.
When we have an oscillating source on the surface of a body of water, a wave is generated that travels out in circular wave fronts in two dimensions. The amplitude of the wave (the actual direction of the waving) is in a direction that is perpendicular to the surface of the water. So how do we represent such a wave?
One way to represent such a wave is in two dimensions where the amplitude of the wave is represented by grayscale. When the wave has a positive amplitude, the color is white, when the amplitude is zero the color is light gray, and when the amplitude is negative the color is black. This is shown in the animation (position is given in centimeters and time is given in seconds). Restart.
Another way to represent a traveling wave in two dimensions is in three dimensions. After all, there are three dimensions to consider: the propagation (which accounts for two dimensions) and the direction of waving. Click the "check to see three-d mode" check box, then click the "set values and play" to see the three-dimensional representation of the wave.
Which representation do you like? In which one is it easier to "see" the wave's motion? While the three-dimensional representation is the more realistic representation, the pure two-dimensional representation that uses grayscale is certainly easier to view and determine the properties of the wave phenomena.