Glenn,

I may have sent this previously, because it's something you would find interesting, but I don't remember, so;

http://fqxi.org/data/forum-attachments/2008CChristov_WaveMotion_45_154_EvolutionWavePackets.pdf

Abstract

The present paper deals with the effect of dissipation on the propagation of wave packets governed by a wave equation of Jeffrey type. We show that all packets undergo a shift of the central frequency (the mode with maximal amplitude) towards the lower frequencies (‘‘redshift’’ in theory of light or ‘‘baseshift’’ in acoustics). Packets with Gaussian apodization function do not change their shape and remain Gaussian but undergo redshift and spread. The possible applications of the results are discussed.

2007 Elsevier B.V. All rights reserved.

Introduction

The propagation of waves in linear dissipative systems is well studied but most of the investigations are concerned with the propagation of a single-frequency wave. On the other hand, in any of the practical situ- ations, one is faced actually with a wave packet, albeit with a very narrow spread around the central fre- quency. This means that one should take a special care to separate the effects of dispersion and dissipation on the propagation of the wave packet from the similar effects on a single frequency signal.

The effect of dissipation of the propagation of wave packets seems important because their constitution can change during the evolution and these changes can be used to evaluate the dissipation.

Especially elegant is the theory of propagation of packets with Gaussian apodization function.