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