Wave Scattering through Step Down Cascading Junctions

In this paper, we present the scattering of plane waves through two junctions with step-down cascading discontinuities. The solutions in form trapped modes corresponding to discrete eigen values are also presented. We illustrate matching continuity pressure and velocity at edges, conservation energy, convergence/error reflection, reflection transmission incident wave that go wider region. discuss amplitudes by varying dimensions wave-guide structure against number. plot surface contour plots along absolute potential different frequencies where extrema field occur. derive results extra ordinary acoustic (EAT) for existing models. apply Mode Matching Method (MMM) tackle problem. Our model would be beneficial old new models containing cavities junctions. However, these cannot retrieve our proposed geometrical model. will helpful practical exhaust system noise reduction theory.