Apart from its dependence of pressure and temperature, the second viscosity coefficient also depends on the process, that is to say, the second viscosity coefficient is not just a material property. Example: in the case of a sound wave with a definitive frequency that alternatively compresses and expands a fluid element, the second viscosity coefficient depends on the frequency of the wave. This dependence is called the dispersion. In some cases, the second viscosity ζ ζ can be assumed to be constant in which case, the effect of the volume viscosity ζ ζ is that the mechanical pressure is not equivalent to the thermodynamic pressure : as demonstrated below. ∇ ∇ ⋅ ⋅ ( ∇ ∇ ⋅ ⋅ u ) I = ∇ ∇ ( ∇ ∇ ⋅ ⋅ u ) , p ¯ ¯ ≡ ≡ p − − ζ ζ ∇ ∇ ⋅ ⋅ u , However, this difference is usually neglected most of the time (that is whenever we are not dealing with processes such as sound absorption and attenuation of shock waves, where second viscosity coefficient becomes important) by explicitly assuming ζ ζ = 0 . The assumption of setting ζ ζ = 0 is called as the Stokes hypothesis. The validity of Stokes hypothesis can be demonstrated for monoatomic gas both experimentally and from the kinetic theory; for other gases and liquids, Stokes hypothesis is generally incorrect. With the Stokes hypothesis, the Navier–Stokes equations become