... III
D. Rocchesso is with the Dipartimento di Informatica, Università degli Studi di Verona, strada Le Grazie, 37134 Verona - ITALY, Phone: ++39.045.8027979, FAX: ++39.045.8027982, E-mail: rocchesso@sci.univr.it. J. O. Smith is with the Center for Computer Research in Music and Acoustics (CCRMA), Music Department, Stanford University, Stanford, CA 94305, E-mail: jos@ccrma.stanford.edu.
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... tension
Tension'' is defined here for gases as the reciprocal of the adiabatic compressibility of the gas [28, p. 230]. This definition helps to unify the scattering formalism for acoustic tubes with that of mechanical systems such as vibrating strings.
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... tube
There appear to be no tube shapes supporting exact traveling waves other than cylindrical and conical (or conical wedge, which is a hybrid) [36]. However, the Salmon horn family'' (see, e.g., [27,37]) characterizes a larger class of approximate one-parameter traveling waves. In the cone, the wave equation is solved for pressure using a change of variables , where is the distance from the apex of the cone, causing the wave equation for the cone pressure to reduce to the cylindrical case [38]. Note that while pressure waves behave simply as non-dispersive traveling waves in cones, the corresponding velocity waves are dispersive [38].
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... power
Note that corresponds to the average physical power at frequency , where , and the wave variable magnitudes on the unit circle may be interpreted as RMS levels. For , we may interpret the power as the steady state power obtained when exponential damping is introduced into the waveguide giving decay time-constant , where (for the continuous-time case, see [40, p. 48]).
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... real
A complex-valued function of a complex variable is said to be positive real if
1)
2)
Positive real functions characterize passive impedances in classical network theory.
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... ratio
Indeed, in the general case is a diagonal matrix.
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... velocity
The symbols for the variables velocity and force have been chosen to maintain consistency with the analogous acoustical quantities.
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