Plane waves

In the physics of wave propagation, a plane wave (also spelled planewave) is a wave whose wavefronts (surfaces of constant phase) are infinite parallel planes. Mathematically a plane wave takes the form

in which the arbitrary (scalar or vector) function ${\displaystyle \tau \mapsto f(\tau )}$ gives the variation of the wave's amplitude, and the fixed unit vector ${\displaystyle |{\vec {n}}|=1}$ is the wave's direction of propagation. The solutions in ${\displaystyle {\vec {x}}}$ of

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