An alternative to the traveling-wave approach for use in two-port descriptions of acoustics bores

Abstract

For more than a decade, the digital waveguide model for musical instruments has been improved through the simulation of cylindrical and conical bores. But several difficulties remain, such as instabilities due to growing exponentials which appear when two conical bores are connected with decreasing taper. In this paper, an alternative overcoming these difficulties is proposed and can be extended to shapes other than cylinders, cones, and hyperbolic horns. A two-port model with more general state variables than usual traveling waves works efficiently for any shape without discontinuities in cross-section. The equations for connecting separate elements at discontinuities make this two-port model appropriate for use in time domain simulation of the physical behavior of the wind instrument and its interactions with the player. The potential of this new approach is illustrated by several detailed examples.