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Horns as Waveguides

Waves in a horn can be analyzed as one-parameter waves, meaning that it is assumed that a constant-phase wavefront progresses uniformly along the horn. Each ``surface of constant phase'' composing the traveling wave has tangent planes normal to the horn axis and to the horn boundary. For cylindrical tubes, the surfaces of constant phase are planar, while for conical tubes, they are spherical [360,320,145]. The key property of a ``horn'' is that a traveling wave can propagate from one end to the other with negligible ``backscattering'' of the wave. Rather, it is smoothly ``guided'' from one end to the other. This is the meaning of saying that a horn is a ``waveguide''. The absence of backscattering means that the entire propagation path may be simulated using a pure delay line, which is very efficient computationally. Any losses, dispersion, or amplitude change due to horn radius variation (``spreading loss'') can be implemented where the wave exits the delay line to interact with other components.

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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2014-03-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University