Planck-Einstein-de Broglie type relations for the acoustic waves

TL;DR

This paper derives analogs of Einstein, Planck, and de Broglie relations for acoustic waves, revealing an equivalent mass, energy-momentum relations, and wave properties similar to quantum mechanics.

Contribution

It introduces a novel framework linking acoustic wave properties to fundamental quantum-like relations, highlighting an equivalent mass and energy-momentum analogs.

Findings

Existence of an equivalent mass for acoustic waves

Derivation of Einstein-like energy-mass relation for waves

Establishment of de Broglie-type momentum-wave number relation

Abstract

In this paper we prove, by expressing the energy as a function of the wave propagation speed, it is highlighted the existence of an equivalent mass of the wave, as well as of an Einstein type relations between the energy and this mass. Also, we establish a relation between angular frequency and energy similar to that of the Planck relation. For the propagating wave, there is a de Broglie type relationship between the linear momentum and the action variable (the angular momentum), i.e. the wave linear momentum is proportional to the wave number, the proportionality coefficient being the action.