On the conservation of momentum for a sound pulse reflecting from a pressure-release boundary.
When a "massless" one-dimensional sound pulse (mass of a sound pulse is defined as an integral of the perturbation of density over the pulse length) reflects from a pressure-release boundary, its momentum changes sign. This obviously violates momentum conservation. However, in contrast to the case of an unbounded medium, calculation of the momentum in a bounded region includes a second-order term as well. Apparently, the second-order correction to the linear solution ensures momentum conservation in this case. The purpose of this Letter is to find a concrete form of this second-order correction. It appears that, as a result of the nonlinear interaction of the pulse with a pressure-release boundary, the latter experiences second-order net shift. This leads to the generation of a massive second-order rarefaction pulse whose momentum is directed opposite to the direction of propagation of the pulse itself. Appearance of this pulse ensures total momentum conservation.
Physical Science Division, NOAA/Earth System Research Laboratory, 325 Broadway, Boulder, Colorado 80305, USA. alexander.voronovich@noaa.gov
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D007700:Kinetics; D008433:Mathematics; D008962:Models, Theoretical; D009038:Motion; D011312:Pressure; D013016:Sound; D013816:Thermodynamics