Momentum
Acoustic waves

A disturbance in a medium gives rise to oscillations, or waves, that propagate away from their source. In a fluid, small changes in pressure p can often be described by the acoustic wave equation:

∂ 2 p ∂ t 2 = c 2 ∇ 2 p, {\displaystyle {\frac {\partial ^{2}p}{\partial t^{2}}}=c^{2}\nabla ^{2}p\,,}

where c is the speed of sound. In a solid, similar equations can be obtained for propagation of pressure (P-waves) and shear (S-waves).

The flux, or transport per unit area, of a momentum component ρ v by a velocity v is equal to ρ v v. In the linear approximation that leads to the above acoustic equation, the time average of this flux is zero. However, nonlinear effects can give rise to a nonzero average. It is possible for momentum flux to occur even though the wave itself does not have a mean momentum.
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