Stokes's law of sound attenuation

In acoustics, Stokes's 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 α given by $${\displaystyle \alpha ={\frac {2\eta \omega ^{2}}{3\rho V^{3}}}}$$ where η is the dynamic viscosity coefficient of the fluid, ω is the sound's angular frequency, ρ is the fluid density, and V is the speed of sound in the medium.^[1]

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]