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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.

Figure 2.12: Extracting a physical signal from a digital waveguide using delay-line taps.

Figure 2.13: More detailed diagram of Fig.2.12.

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 [479], 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 [265]. However, as derived in Appendix CC.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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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4
Copyright © 2023-08-20 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University