Waves in 2D and 3D
i.) Basic Parameters: ω, λ, T, c, and A:
The same parameters are used to represent waves in 2D and 3D that
are used in 1D. One difference is that in dimensions 2 or greater,
the wavelength λ is a vector.
This diagram illustrates some of the different parameters of a wave
Graphical Representation of Waves in 2D:
A wavefront is a line (in 2D) or a surface (in 3D) on which every
point is at the same phase while a ray is a line perpendicular to
the wavefront which shows the wave's direction of travel. The following
diagram illustrates this.
ii.) Equations of Waves in 2D & 3D
Equation of the Wave in 2D:
f(x,y) = Acos(ax + by - ωt)
Equation of the Wave in 3D:
f(x,y, z) = Acos(ax + by + cz - ωt)