Chapter 9 - Problems

Abstract

This chapter addresses several problems related to acoustics. One of the problems is related to eigenmodes for the dirichlet problem. In this it is assumed that the acoustic pressure satisfies a homogeneous Dirichlet condition along the boundary σ of the propagation domain. Another problem is related to forced regime for the Dirichlet problem; in this the eigenmodes series expansion of the sound pressure p(x, y, and z) is established, which satisfies the corresponding non-homogeneous Helmholtz equation. In the Green's representation of the exterior Dirichlet and Neumann Problems, the boundary integral equations are deduced. In the problem related to Fourier transform and separation method, the one plane is described by a homogeneous Dirichlet condition, the other one by a homogeneous Neumann condition; it is observed that the method of spatial Fourier transform and the method of separation of variables lead to the same solution.