Abstract
The present research is centered on analyzing and modeling the scattering characteristics of a trifurcated waveguide that includes impedance discontinuities. A mode-matching method, grounded in projecting the solution onto orthogonal basis functions, is devised for the investigation. The impedance disparities at the interfaces are represented in normal velocity modes, which, when combined with pressure modes, result in a linear algebraic system. This system is subsequently truncated and inverted for numerical experimentation. The convergence of scattering amplitudes is assured by reconstructing matching conditions and adhering to conservation laws. The computational results indicate that optimizing attenuation behavior is achievable through manipulating variation bounding properties and impedance discontinuities.