9.1. Introduction

This chapter deals with the problems of acoustics in closed spaces, more precisely in domains (D) delimited by closed surfaces (S). There are different approaches as to the treatment of such problems depending on the accuracy required, a function of the geometry and dimensions of the considered spaces, and the objective of the problem at hand.

In relation to dimensions and geometry, cavities can be divided into four groups: the "miniature" cavities (where one of the dimensions is of the same order of magnitude as the visco-thermal boundary layers; sections 3.6 to 3.10); the small cavities (where the dimensions are significantly smaller than the considered wavelengths, but remain far larger than the boundary layers; sections 3.5 and 6.3.2.2); the cavities, the dimensions of which are of the same order of magnitude as the considered wavelengths (which require a modal approach, presented here while assuming separable geometry); and finally, the cavities (or rooms) the dimensions of which are larger than the wavelengths considered and where modal theory becomes prohibitive due to the high number of modes to consider.

In practice, and particularly in the case of rooms, the methods most frequently used require a numerical approach relying on Finite Elements or Boundary Elements analysis, methods of the layer potentials, image sources, rays or statistical analysis (Statistical Energy Analysis (SEA)). Only modal and statistical methods are presented in this chapter.

The objective in this chapter is to present the application of modal analysis to acoustic cavities, assuming dissipation during the...