Scattering of Elastic Waves in a Quasi-one-dimensional Cavity: Theory and Experiment

TL;DR

This paper investigates the scattering of torsional elastic waves in a quasi-one-dimensional cavity through combined experimental and theoretical approaches, demonstrating excellent agreement and drawing parallels to quantum scattering phenomena.

Contribution

It provides a comprehensive analysis of elastic wave scattering in a cavity, deriving the scattering matrix and validating it with experiments, linking classical elastic waves to quantum scattering models.

Findings

The scattering matrix S follows Poisson's kernel distribution.

Experimental results match theoretical predictions with high accuracy.

The elastic wave scattering resembles quantum delta potential scattering.

Abstract

We study the scattering of torsional waves through a quasi-one-dimensional cavity both, from the experimental and theoretical points of view. The experiment consists of an elastic rod with square cross section. In order to form a cavity, a notch at a certain distance of one end of the rod was grooved. To absorb the waves, at the other side of the rod, a wedge, covered by an absorbing foam, was machined. In the theoretical description, the scattering matrix S of the torsional waves was obtained. The distribution of S is given by Poisson's kernel. The theoretical predictions show an excellent agreement with the experimental results. This experiment corresponds, in quantum mechanics, to the scattering by a delta potential, in one dimension, located at a certain distance from an impenetrable wall.