Acoustics in the Lagrange picture: an application to the Rayleigh radiation pressure
Résumé
At the undergraduate level, most lectures and textbooks on hydrodynamics make use of the so-called Euler picture, where the pressure, temperature and velocity of the fluid are treated as continuous fields defined by the value they take at each point of the reference frame the fluid moves in. There nevertheless exists another possible description of the movement which consists in labelling the fluid elements themselves, and keeping this labelling in the course of the motion. This so-called Lagrange picture is scarcely taught for it often introducess more complicated mathematics, as soon as a three-dimensional geometry is considered. Yet it is actually more intuitive than the Euler picture. In this paper, we illustrate the point in the example of the Rayleigh acoustic radiation pressure. An improved physical insight ensues, which is of interest to students graduating in acoustics.
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