Analog model for thermoviscous propagation in a cylindrical tube

Abstract

Modeling acoustic propagation in tubes including the effects of thermoviscous losses at the tube walls is important in applications such as thermoacoustics, hearing aids, and 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 cylindrical tube model based on a continued fraction expansion of the thermal and viscous functions. The model can be represented as an analog circuit model which allows its use in time domain system modeling. This model avoids problems with fractional derivatives in the time domain.