Editing Plane wave (section)

===Plane standing wave ===

A [[standing wave]] is a field whose value can be expressed as the product of two functions, one depending only on position, the other only on time.  A [[plane standing wave]], in particular, can be expressed as
<math display="block">F(\vec x, t) = G(\vec x \cdot \vec n) \, S(t)</math>
where <math>G</math> is a function of one scalar parameter (the displacement <math>d = \vec x \cdot \vec n</math>) with scalar or vector values, and <math>S</math> is a scalar function of time.  

This representation is not unique, since the same field values are obtained if <math>S</math> and <math>G</math> are scaled by reciprocal factors. If <math>\left|S(t)\right|</math> is bounded in the time interval of interest (which is usually the case in physical contexts), <math>S</math> and <math>G</math> can be scaled so that the maximum value of <math>\left|S(t)\right|</math> is 1.  Then <math>\left|G(\vec x \cdot \vec n)\right|</math> will be the maximum field magnitude seen at the point <math>\vec x</math>.