 ... 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, Email:
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, Email:
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 oneparameter
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 nondispersive
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 timeconstant ,
where
(for the continuoustime case, see [40, p. 48]).
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 ... real^{}
 A complexvalued 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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