American Institute of Physics for the Acoustical Society of America
Journal of the Acoustical Society of America vol:119 issue:2 pages:751-755
Dispersion due to internal frictions as wave propagates is a consequence of the second principle of thermodynamics. When the wavelengths are several times higher than the mesoscopic inhomogeneities, internal diffractions can be ignored and the propagation medium can then be considered as a continuum at the scale of these wavelengths. Here, we consider the dissipation mechanism due to viscosity only. By mean of Laplace transforms both on time and space, a causal analysis leads us to a closed-form solution, which we think is the simplest analytical form. This is illustrated by searching the viscoelastic Green's function associated with the horizontal shear wave generated by a uniform impulsive line source in an infinite homogeneous medium, whose example is almost mathematically equivalent to the study of the scalar wave generated in viscous fluid. The described method is thus restricted to one-wave propagation problems and is probably not generally applicable when the source generates several waves. In the course to obtain a transient analytical expression of pulsed wave through a dispersive medium, this study proposes a method for transient cylindrical waves, while most previous methods concern plane waves. (c) 2006 Acoustical Society of America.