The law and its derivation were published in 1845 by the Anglo-Irish physicist G. G. Stokes, who also developed Stokes's law for the friction force in fluid motion. A generalisation of Stokes attenuation taking into account the effect of thermal conductivity was proposed by the German physicist Gustav Kirchhoff in 1868.[2][3]
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]
^ a bStokes, G.G. "On the theories of the internal friction in fluids in motion, and of the equilibrium and motion of elastic solids", Transactions of the Cambridge Philosophical Society, vol.8, 22, pp. 287-342 (1845)
^G. Kirchhoff, "Ueber den Einfluss der Wärmeleitung in einem Gase auf die Schallbewegung", Ann. Phys., 210: 177-193 (1868). Link to paper
^S. Benjelloun and J. M. Ghidaglia, "On the dispersion relation for compressible Navier-Stokes Equations," Link to Archiv e-print Link to Hal e-print
^Happel, J. and Brenner, H. "Low Reynolds number hydrodynamics", Prentice-Hall, (1965)
^Landau, L.D. and Lifshitz, E.M. "Fluid mechanics", Pergamon Press,(1959)
^Morse, P.M. and Ingard, K.U. "Theoretical Acoustics", Princeton University Press(1986)
^Dukhin, A.S. and Goetz, P.J. "Characterization of liquids, nano- and micro- particulates and porous bodies using Ultrasound", Edition 3, Elsevier, (2017)
^Litovitz, T.A. and Davis, C.M. In "Physical Acoustics", Ed. W.P.Mason, vol. 2, chapter 5, Academic Press, NY, (1964)