The resulting contribution to sound attenuation is described by the viscous attenuation coefficient α_vis. According to Bhatia [22],

Here c_s denotes the speed of sound, η_s the shear viscosity, η_v the bulk viscosity, f the frequency (f = ω/2π), and ρ the density.

This relationship depends on both frequency and the properties of the medium under investigation. Those properties are primarily characterized by shear and bulk viscosity. Shear viscosity follows from Stokes’ law of friction. In critical liquids, an additional critical contribution must be included; notably, this critical contribution depends on frequency. The total shear viscosity is thus written as

Bulk viscosity is a considerably more complex concept. Compressing a defined volume within a sound wave involves volume work, which appears as an additional contribution to sound absorption. The next subsection considers bulk viscosity in greater detail: when the hard-sphere model is abandoned and molecular structure is taken into account, the conclusions change substantially. In the classical treatment of absorption, η_v is regarded as constant.

2. Attenuation due to thermal conduction and inhomogeneity of the fluid. Thermal conduction provides another source of absorption. In aqueous media its contribution is small compared with α_vis, but it is included here for completeness.