Physical Outputs

Physical variables (force, pressure, velocity, ...) are obtained by summing traveling-wave components, as shown in Fig.1.11.

It is important to understand that the two traveling waves in a digital waveguide are now components of a more general acoustic vibration. The physical wave vibration is obtained by summing the left- and right-going traveling waves. A traveling wave by itself in one of the delay lines is no longer regarded as ``physical'' unless the signal in the opposite-going delay line is zero. Traveling waves are efficient for simulation, but they are not easily measured directly in the physical world [489], except when the traveling-wave component in one direction can be arranged to be zero [433].

For a full derivation of digital waveguide theory starting with the basic wave equation for ideal strings, see Appendix H.

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written by 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.