Wave Phenomena and Wave Equations

TL;DR

This paper discusses deriving wave equations from experimental data across various wave types, emphasizing an experimental approach to matter waves and testing procedures on water waves to understand their dynamics.

Contribution

It introduces an experimental methodology for deriving wave equations from measurements, applicable to different wave phenomena including matter and water waves.

Findings

Dispersion relations can be derived from experiments for various waves.

Wave equations are characterized by the structure of their dispersion relations.

The approach is tested on water waves to validate the methodology.

Abstract

For any kind of wave phenomenon one can find ways to derive the respective dispersion relation from experimental observations and measurements. This dispersion relation determines the structure of the wave equation and thus characterizes the dynamics of the respective wave. Different wave phenomena are thus governed by different differential equations. Here we want to emphasize the experimental approach to matter waves, but before doing so we will discuss and test the procedure for other types of waves, in particular water waves.