Exchange of sound energy between several rooms

Most room acoustics models are based on relationships applicable to a single room isolated from neighboring rooms or from the outside world.

In reality, it is never possible to completely eliminate the exchange of sound energy between the room under study and its environment. However, neglecting the disturbances induced by these exchanges is of no consequence for most cultural venues, as they are generally designed to limit the disturbances they may suffer or induce.

In the case of industrial sites, these approximations are no longer valid, since functional aspects take precedence over all other considerations (auditory and visual comfort, in particular), and it is rarely possible to optimize insulation between the different compartments that make up these sites. What's more, the noise levels induced by certain industries are such that it is impossible to reduce them without incurring exorbitant costs incompatible with the budgets of the companies concerned.

The study of sound energy exchange and cost optimization is therefore an important problem, requiring the implementation of specific models rarely covered in conventional architectural acoustics literature.

To fill this gap, two articles are proposed:

• the present article on the mathematical formulation of coupled systems and the simplified models derived from it;

• a dossier on the specific methodologies used in the approach required to optimize complex models governed by too many variables [BR 1 010][BR 1 012][BR 1 014] .

This first article, on the mathematical formulation of energy exchanges, starts from the basic concepts presented in the article