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Stokes' law of sound attenuation : ウィキペディア英語版
Stokes' law of sound attenuation

Stokes law of sound attenuation is a formula for the attenuation of sound in a Newtonian fluid, such as water or air, due to the fluid's viscosity. It states that the amplitude of a plane wave decreases exponentially with distance traveled, at a rate \alpha given by
: \alpha = \frac
where \eta is the dynamic viscosity coefficient of the fluid, \omega is the sound's frequency, \rho is the fluid density, and V is the speed of sound in the medium:〔Stokes, G.G. "On the theories of the internal friction in fluids in motion, and of the equilibrium and motion of elastic solids", ''Transaction of the Cambridge Philosophical Society'', vol.8, 22, pp. 287-342 (1845〕
The law and its derivation were published in 1845 by physicist G. G. Stokes, who also developed the well-known Stokes' law for the friction force in fluid motion.
==Interpretation==
Stokes' law applies to sound propagation in an isotropic and homogeneous Newtonian medium. Consider a plane sinusoidal pressure wave that has amplitude A_0 at some point. After traveling a distance d from that point, its amplitude A(d) will be
:A(d) = A_0e^
The parameter \alpha is dimensionally the reciprocal of length.
In the International System of Units (SI), it is expressed in neper per meter or simply reciprocal of meter (\mathrm^). That is, if \alpha = 1 \mathrm^, the wave's amplitude decreases by a factor of 1/e for each meter traveled.

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