An original model based on first principles is constructed for the temporal correlation of acoustic waves propagating in random scattering media. The model describes the dynamics of wave fields in a previously unexplored, moderately strong (mesoscopic) scattering regime, intermediate between those of weak scattering, on the one hand, and diffusing waves, on the other. It is shown that by considering the wave vector as a free parameter that can vary at will, one can provide an additional dimension to the data, resulting in a tomographic-type reconstruction of the full space-time dynamics of a complex structure, instead of a plain spectroscopic technique. In Fourier space, the problem is reduced to a spherical mean transform defined for a family of spheres containing the origin, and therefore is easily invertible. The results may be useful in probing the statistical structure of various random media with both spatial and temporal resolution.

In this work we present the design and the manufacturing processes, as well as the acoustics standardization tests, of an acoustic barrier formed by a set of multi-phenomena cylindrical scatterers. Periodic arrangements of acoustic scatterers embedded in a fluid medium with different physical properties are usually called Sonic Crystals. The multiple scattering of waves inside these structures leads to attenuation bands related to the periodicity of the structure by means of Bragg scattering. In order to design the acoustic barrier, two strategies have been used: First, the arrangement of scatterers is based on fractal geometries to maximize the Bragg scattering; second, multi-phenomena scatterers with several noise control mechanisms, as resonances or absorption, are designed and used to construct the periodic array. The acoustic barrier reported in this work provides a high technological solution in the field of noise control.