Lagrangian Sound

At least at the undergraduate level, most lectures and textbooks about hydrodynamics make use of the so-called Eulerian picture, where pressure, temperature, velocity of the fluid are treated as continuous fields defined by the value they take at each geometrical point of the reference frame the fluid moves in. There nevertheless exists another possible description of the movement which consists in labelling the fluid element themselves, and keep this labelling in the course of the motion. This so-called Lagrangian picture is scarcely taught for it often brings in somehow involved mathematics, although it occurs to be more intuitive than the Eulerian picture. In this paper, we try to illustrate the latter feature on the exemple of the otherwise cumbersome problem of the Rayleigh acoustic radiation pressure, and we argue that dealing with the mathematical difficulties implied by the Lagrangian picture may be a good pedagogical opportunity to familiarize with tensorial calculus