Simulação da propagação de ondas acústicas através de uma malha de guias digitais de ondas

Abstract

This work was developed looking at the construction of a computational tool, aimed to the acoustic modeling of reverberation environment. In this way, it was necessary to elaborate a numerical system able to simulate the wave sound propagation and, mainly its interactions with the surfaces encountered in the analyses. These interactions represent the basic wave phenomena, that can well defined by the reflection, transmission and absorption of sound waves by the obstacles. After a thoroughly research about the methodologies applied on the resolution of the problem, and keeping in mind the mathematical characteristics required for the system, the Digital Waveguide Mesh was chosen for the base of the whole development of the algorithm proposed. The Digital Waveguides can be treated as a numerical system based on the known d Alembert solution for the General Wave Equation. Therefore, it can be easily handle to describe the one-dimensional sound wave propagation, between any two points in the space. The mesh was built through the interconnection of several Digital Waveguides, defining so the wanted geometries. Finally, the solution of the problem is obtained for each point, through the mathematical formulation of the scattering junctions, whose represent the interception points of the waveguides, in which will be expressed the values associated with the analyzed phenomena. The whole formulation is based on the impedance properties of the environment, that is, the wave movement is carried through the transmissions, absorption and the reflection of the acoustics waves, by the scattering junctions. In this work, it was tested different kinds of mesh, in several configurations, in way to explore the critical points of the use of the methodology proposed. The results gotten by the Digital Waveguide Mesh had shown satisfactory in all of the analyzed cases, fact that, added to the simplicity of the algorithm, brings our eyes the efficiency and the easy handling of the method in the resolution of the considered problem.