In a trabecular bone, considered as a nondissipative porous medium, the scattering of an incident wave by cylindrical pores larger than the wavelength is studied. The goal is to know if scattering alone may cause such a high attenuation as that observed in calcaneus. The porous medium is modelized via Biot's theory and the scattering by a single pore is characterized from the definition of a scattering matrix. An approximation of weakly disordered medium is then discussed to estimate the effective attenuation and dispersion as a function of frequency. These effective properties are shown to be different of those measured on calcaneus, due to the neglect of wave conversions during the scattering process.

For in vacuo elastic plates or plates fluid-loaded on one side, it has been previously shown that dispersion curves for both plate-borne (Lamb) type and, in the latter case, also fluid-borne (Scholte–Stoneley) type fail to cross but repel each other, with the waves simultaneously exchanging their physical character. This study is extended here to the case of a plate loaded by two different fluids, where a quantitative calculation of dispersion curves for water on one side, and a lighter or a heavier fluid on the other, is carried out confirming the existence of two different Scholte–Stoneley waves.

The subject of propagating waves on fluid-loaded plates and shells, and their acoustic excitation, has become of great current interest. Besides the existence of the Lamb-type plate or shell wave modes, a water-borne Scholte-Stoneley wave has been found on plates or shells specifically with one-sided water loading. Another specific case is that with two-sided water (or same-fluid) loading; here a symmetrical Scholte-Stoneley wave was found in addition to an antisymmetric one. In this paper, more generally, the plate loaded with two different fluids is discussed via the corresponding dispersion curves of plate and fluid-borne waves. The existence of two Scholte-Stoneley waves has been confirmed for this case.

The Foldy and the Waterman and Truell approximations are used to determine the effective properties of the coherent wave that emerges after multiple scattering of a plane longitudinal fast wave by the largest pores in a trabecular bone. The unit scattering cell considered is either a single pore or two close cylindrical pores (cluster), at a fixed overall bone porosity. In the cluster case, the effective attenuation is about twice that obtained with one single pore per scatterer. It is shown that taking into account the marrow viscosity leads only to minor differences on the effective dispersion and attenuation.