A thermoviscous tube propagation model suitable for time domain analysis

Modeling acoustic propagation in tubes including the effects of thermoviscous losses at the tube walls is important in thermoacoustics, in hearing aid modeling and in modeling wind musical instruments. Frequency dependent impedances for a tube transmission line model in terms of the so-called thermal and viscous functions are well established, and form the basis for frequency domain analysis of systems that include tubes. However, frequency domain models cannot be used for systems in which significant nonlinearities are important, as is the case with the pressure-flow relationship through the reed in a woodwind instrument. This paper describes a tube model based on a continued fraction expansion of the thermal and viscous functions. The expansion can be represented as an analog circuit model which allows its use in time domain system modeling. A simple model of a clarinet-like oscillation will be shown.