Spectral quality of acoustic predictions obtained by the ray method in coupled two-dimensional damped cavities

Numerical modelling of coupling in acoustics in the medium-frequency range poses problems, which remain to be solved. Indeed, in such cases, finite element methods in volumes or on boundaries generate too large a number of degrees of freedom due to the size of the domains (the volumes or the boundaries). With the ray method in simple convex damped cavities, it is possible to target a small number of points inside the domain and, subsequently, to economize on calculation time, making it possible to look for spectral instead of harmonic results. Does this still hold when damped cavities are coupled by an acoustic transmission path or by a vibrating structure, with aural perception in view? In fact, due to inherent approximations, the ray method is inaccurate in the presence of absorbent walls and thus in damped coupled cavities. However, an analysis will show that a hierarchy exists among the errors arising from the rays, and finally it will appear that only the grazing rays must be replaced by another approximation. In these conditions, the ray method is capable of solving coupling problems in acoustics in the medium-frequency range with greater computing speed than finite element methods.