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Wave Phenomena

Figure: Two views of a wave.

We can visualize a vivid example for the sake of illustration: suppose the "amplitude" $A$ is the height of the water's surface in the ocean (measured from $A=0$ at "sea level") and $x$ is the distance toward the East, in which direction waves are moving across the ocean's surface.^14.1Now imagine that we stand on a skinny piling and watch what happens to the water level on its sides as the wave passes: it goes up and down at a regular frequency, executing SHM as a function of time. Next we stand at a big picture window in the port side of a submarine pointed East, partly submerged so that the wave is at the same level as the window; we take a flash photograph of the wave at a given instant and analyze the result: the wave looks instantaneously just like the graph of SHM except the horizontal axis is distance instead of time. These two images are displayed in Fig. 14.1.

Footnotes

. . . surface.^14.1

Technically speaking, I couldn't have picked a worse example, since water waves do not behave like our idealized example - a cork in the water does not move straight up and down as a wave passes, but rather in a vertical circle. Nevertheless I will use the example for illustration because it is the most familiar sort of easily visualized wave for most people and you have to watch closely to notice the difference anyway!