Sound attenuation in fluids is also accompanied by acoustic dispersion, meaning that the different frequencies are propagating at different sound speeds.[1]
Interpretation
Stokes's law of sound attenuation applies to sound propagation in an isotropic and homogeneous Newtonian medium. Consider a plane sinusoidalpressure wave that has amplitude A0 at some point. After traveling a distance d from that point, its amplitude A(d) will be
The law is amended to include a contribution by the volume viscosityζ:
The volume viscosity coefficient is relevant when the fluid's compressibility cannot be ignored, such as in the case of ultrasound in water.[4][5][6][7] The volume viscosity of water at 15 C is 3.09 centipoise.[8]
Modification for very high frequencies
Stokes's law is actually an asymptotic approximation for low frequencies of a more general formula involving relaxation timeτ:
Dukhin, A.S. and Goetz, P.J. "Characterization of liquids, nano- and micro- particulates and porous bodies using Ultrasound", Edition 3, Elsevier, (2017)