Solution to Waves in Dissipative Media with Reciprocal Attenuation in Time and Space Domains

TL;DR

This paper introduces a new general solution for dissipative wave equations using Fourier transform, demonstrating simultaneous attenuation in time and space, and highlighting how different attenuation mechanisms affect wave properties.

Contribution

A novel general solution to dissipative wave equations is proposed, revealing the dual-domain attenuation and its impact on wave behavior.

Findings

Attenuation occurs simultaneously in time and space domains.

Different attenuation mechanisms lead to different wave properties.

The new solution provides a more comprehensive understanding of dissipative waves.

Abstract

The study points out that the traditional solutions to wave equation of dissipative wave and motion equation of block for a multi-degree-of-freedom mass spring damper system are the possible solutions, which are not necessarily objective and conflict each other. The disturbance in discrete system like crystals vibration can be expressed in differential form. A new general solution to dissipative wave equation is proposed with the general Fourier transform. The solution reveals that the attenuation of the disturbance can simultaneously occur in time and space domains. Then the general solution is used in case studies to analyze the properties of dissipative waves. It is concluded that the properties of waves formulated with the same equation can be different because of the difference of attenuation mechanism.