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