Sound Attenuation and Prediction of Porous Media Properties in Hybrid Ducts Utilizing Spatially Periodic Area Changes

A theory based on cross-sectional averaging is developed to analyze quasi-one-dimensional acoustic propagation in hybrid ducts with two propagation media in the cross-section. Specifically, ducts lined with a thick layer of porous material are considered. The porous material makes the duct wavenumber complex, changing the phase speed and introducing attenuation. To lowest order, the wavenumber depends only on the ratio of cross-sectional areas and the properties of the constituent media, and surprisingly not on the material configuration in the cross-section. High frequency accuracy can be improved by using a small correction that includes shape coefficients that depend on the cross-sectional configurations. If the propagation wavenumber is measured experimentally in a hybrid duct, the complex effective sound speed and density, fundamental porous material properties, can be extracted relatively easily. Experimentally, open cell foam samples line the sides of a tube closed at one end, and the complex wavenumber is determined from standing wave measurements. The cross-sectional averaging theory is then used to determine the acoustic properties of the open-cell foam. Results are compared for various lining configurations to assess the accuracy of the method. Another application of this work is the theoretical and experimental study of the propagation of quasi one-dimensional acoustic waves through a duct with spatially periodic area changes. This configuration exhibits stop-band and pass-band behavior, with substantially reduced sound transmission in stop bands, but little effect in pass bands. The regions of the duct with larger cross-sectional area are partially filled with an annular region of porous material to provide pass-band attenuation, leaving a constant area passage for airflow. Predictions and measurements for hybrid ducts with periodic area changes are presented. A muffler designed to place engine harmonics in targeted stop-bands is described.