3D Sound

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 [158] and wave field synthesis [49].

Consider a point source at position . Then the acoustic complex amplitude at position is given by

where denotes the complex amplitude one meter from the point source in any direction, and denotes the wavenumber (spatial radian frequency). Distributed acoustic sources are handled as a superposition of point sources, so the point source is a completely general building block for all types of sources in linear acoustics.

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.

---

Previous: 2D Boundary Conditions
Next: Digital Waveguide Theory

Order a Hardcopy of Physical Audio Signal Processing

---

About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.