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

TL;DR

This paper models sound as a self-consistent phonon field in a continuous medium, drawing an analogy to superconductivity, and explains experimental Fletcher-Munson curves through this theoretical framework.

Contribution

It introduces a novel tensor-based phonon field description and links it to superconducting states, providing a new theoretical explanation for sound perception curves.

Findings

Energy density of phonon field proportional to pressure squared and frequency

Exact wave solutions derived from the Kadić-Edelen Lagrangian

Analogous behavior between phonon field and superconducting electromagnetic state

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.