Abstract
Present communication addresses the scattering of the dominant acoustic wave mode propagating from a semi-rigid waveguide. The underlying waveguide is tuned because of trifurcated inlet regions whereas outer surfaces are flexural. The matching of the scattering duct modes (orthogonal and non-orthogonal) is accomplished by employing continuity of pressure and velocity across the interface. The reflection and transmission coefficients are calculated using mode matching methods. The obtained infinite linear algebraic systems are truncated and solved numerically. The expressions for energy functionals in different duct regions are obtained and sketched subject to different parameters of interest. Through mathematical and graphical illustrations, the obtained solution is authenticated with the law of energy conservation and verification of geometric conditions.