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Stokes' law (sound attenuation)
Additional recommended knowledge
According to this law attenuation of sound α is proportional to the dynamic viscosity η, square of the sound frequency ω, and reciprocally proprtional to the liquid density ρ and cubic power of sound speed V
Attenuation is expressed in neper per centimeter in this equation. The author of this law is the same famous Stokes who derived well known Stokes' law for the friction force in fluids. It is 160 years old. This remarkable law does not contain unknown or un-measurable parameters.
There has been substantial theoretical development in this field since Stokes’ pioneering work. It has brought one important correction to the Stokes law. It turns out that in addition to the dynamic viscosity the parameter of volume viscosity ηv also affects the total attenuation according to the following relationship:
The parameter volume viscosity is surprisingly little known despite its fundamental role for fluid dynamics at high frequencies. This parameter appears in Navier-Stokes equation if it is written for compressible fluid, as described in the most books on general hydrodynamics , , and the acoustics , .
This volume viscosity coefficient becomes important only for such effects where fluid compressibility is essential and, importantly, ultrasound propagation is one such effect. Indeed, many rheological texts just assume the fluid to be incompressible and the volume viscosity therefore plays no role.
The only values for the volume viscosity of simple Newtonian liquids known to us come from the old Litovitz and Davis review . They report a volume viscosity of water at 15 C0 equals 3.09 centipoise
where relaxation time τ equals:
Corresponding relaxation frequency is about 1000 GHz. It is extremely high. For all practical puposes of describing sound attenuation in Newtonian liquids Stokes' law is clearly suffucient.
|This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Stokes'_law_(sound_attenuation)". A list of authors is available in Wikipedia.|