The mathematics of 3D sound is quite elementary, as we will see below. The hard part of the theory of practical systems typically lies in the mathematical approximation to the ideal case. Examples include Ambisonics  and wave field synthesis .
Consider a point source at position . Then the acoustic complex amplitude at position is given by
The fundamental approximation problem in 3D sound is to approximate the complex acoustic field at one or more listening points using a finite set of loudspeakers, which are often modeled as a point source for each speaker.
FDA of the Ideal String
2D Boundary Conditions