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Mathematics 309

Part I - The elementary geometry of wave motion

Waves in 2D and 3D

In 2D a wave is the propagation of simple periodic motion with crests along lines.

The parameters are as in 1D amplitude A, wave length , velocity c, period T, and frequency f. But here both the velocity and the wave length should be taken to be vectors.

  • In time T, one wavelength passes by a fixed point, so that the original crest shifts by a vector . Therefore we have an identity of vectors c = /T.

The equation of the wave height is

y = A cos (ax+by+cz-t)

where is as before the radian frequency. But now ax+by = 2 .[x,y] /| |2