Harmonic Waves -- from Eric Weisstein's World of Physics

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Harmonic Waves

From harmonic addition theorem, Eric Weisstein's World of Math any superposition of harmonic waves

is itself a harmonic wave

where

and

If the waves are coherent so that they all have the same amplitude and phase, then for all i and j, so

and (3) becomes

Assume that all waves are incident with the same amplitude. For a sufficiently large number of randomly oriented phases ,

and (3) becomes