Description of sound as a self-consistent field in continuous media, analogous to a superconducting state. Theoretical explanation of the experimental Fletcher-Munson curves

Abstract

We introduce a description of sound waves using the phonon field equivalent to a 4 dimensional second-rank tensor of distortion similar to electromagnetic waves, which are described by a 4-vector of the electromagnetic field. The exact wave solutions of the state equations of the Kadi\'c-Edelen Lagrangian are obtained for the phonon field in a continuous isotropic medium. We demonstrate that the state of the medium with the phonon field is analogous to the self-consistent superconducting state of the electromagnetic field described by the London equation. It is shown that the energy density of the phonon field in the air is proportional both to the quares of pressure and of frequency, which corresponds to the experimental Fletcher-Munson curves.