Modeling quasi-one-dimensional sound propagation in ducts having two propagation media using a cross-sectional averaging theory

Abstract

Sound propagation of quasi-one-dimensional waves through a uniform duct partially filled with porous material has been studied theoretically and experimentally. The porous material makes the effective propagation wave number in the duct complex. A fairly simple theory based on cross-sectional averaging is derived and tested and found to work extremely well up to fairly high frequency. Interestingly, the basic theory depends only on the ratio of cross-sectional areas and the properties of the individual propagation media, but not on the specific configuration of material in a cross section. A higher order correction is developed to achieve excellent accuracy to very high frequency. This correction includes a coefficient that does depend on the specific cross-sectional configuration. Results are compared to exact solutions for layered and annular configurations, and also to experimental measurements with open cell foam as the porous material. An interesting application is to use measured wave numbers to predict the complex effective density and sound speed of porous media samples partially filling the duct. Other applications include fairly simple improved predictions of the behavior of sound in ducts lined with, or partially filled with, bulk reacting absorbing material.