Translations:The wave equation/2/en

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What is a plane wave? A plane wave is perhaps the simplest example of a 3D wave. It exists at a given instant and can be visualized as a propagating plane surface of constant phase, so that the plane surface remains perpendicular to a given direction of propagation. A plane wave is essentially one-dimensional because spatial variation occurs only along the direction of propagation. We have quite practical reasons for studying this sort of disturbance, one of which is that an actual observed spherical wave can be decomposed into its constituent plane waves. This procedure is called plane-wave decomposition, and it is useful because plane waves have much simpler properties than spherical waves do. The special significance of this approach is that any 3D wave can be expressed as a combination of plane waves, each having a distinct amplitude and direction of propagation. Of all the 3D waves, only the plane wave (whether it is sinusoidal or not) moves through space with an unchanging profile.