Physical Outputs

Physical variables (force, pressure, velocity, ...) are obtained by summing traveling-wave components, as shown in Fig.2.12, and more elaborated in Fig.2.13.

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 estimated from real-world measurements [476], except when the traveling-wave component in one direction can be arranged to be zero.

Note that traveling-wave components are not necessarily unique. For example, we can add a constant to the right-going wave and subtract the same constant from the left-going wave without altering the (physical) sum [263]. However, as derived in Appendix C (§C.3.6), 1D traveling-wave components are uniquely specified by two linearly independent physical variables along the waveguide, such as position and velocity (vibrating strings) or pressure and velocity (acoustic tubes).

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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.