Malin's Magnificent Math

Scaling & Shifting of Graphs

Elementary Waves

Affine Functions

Waves in 2D & 3D

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 in 2D.


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)