Elastic waves through a packing of spheres

Abstract Based on a theory of porous solids previously developed by the author, the elasticity of a hexagonal close packing of equal spheres is treated. The packing is anisotropic and because of the weight of the spheres, also inhomogeneous. The velocities of propagation of elastic waves have been calculated for evacuated interspaces and for interspaces filled with a liquid or gas. In the case of evacuated or air-filled interspaces, the wave rays and travel times have been computed. The packing which has been treated may be of use as a model for a dry or wet loose material such as gravel or sand. Though the model is very simplified, the results obtained show some typical effects such as anisotropy, inhomogeneity, and a 90 degrees angle of emergence.