Abstract : A theoretical study of double panels acoustic transparency based on a patch mobility method is presented and compared with experiment. Boundary diffuse field is also characterize with a new index that explains inter-laboratory problems of reproductibility. Granular materials are then studied with a new model based on a simplification of Biot's model that yields to a gain in time of computation. Inverse measurements with several models are also presented to characterize such materials. Finally improvement of acoustic transparency with mechanical links by optimising their location is studied, and theoretical solutions are compared with experiments.