Scattering of acoustic waves through porous media in a continuous spectrum

The mode-matching technique is employed to analyze acoustic wave propagation in a duct system comprising porous materials in the inlet and outlet regions, and a compressible fluid in the central section. The lower wall of all duct sections is assumed to be rigid, while the inlet and outlet regions are fully bounded by rigid surfaces. The central region consists of two vertical membranes connected to a horizontal membrane, forming a coupled flexible boundary system. The influence of three types of edge conditions, namely zero-displacement, zero-gradient, and spring-like conditions, applied at the joints (± L , p ), where p = 0, b , is systematically investigated. Their effects on transmission loss, absorbed power, and scattering energies are evaluated for three porous materials: A-glass, E-glass, and basalt wool. The results indicate that A-glass exhibits superior sound absorption performance compared to the other materials across all considered edge conditions. Furthermore, A-glass demonstrates enhanced transmission loss over the entire frequency range. It is also observed that spring-like edge connections significantly improve the acoustic performance of the duct by increasing sound attenuation. The validity of the solution is confirmed through energy conservation and the reconstruction of matching conditions at the respective joints.