Theoretical Lossless Wave Propagation

[inflector]

I'm working on trying to understand wave propagation. In particular, I'm trying to understand directional wave propagation in elastic and inelastic materials.

Is there an ideal theoretical medium in which it is possible to propagate waves in an entirely directional i.e. straight-line manner so that the energy could be picked up at the other end of the medium? What would the properties of this ideal medium have to be?

Another way to get at the same issue is to ask what properties of real substances cause them to diverge from this ideal medium?

Thanks,

Curtis

 

[torquil]

Well, first of all the forces that acts between the units in a real lattice are not completely harmonic, so there is a deviation from the wave equation right there. In addition, the lattice is not perfect, leading to a spreading of the wave, and also to the fact that the atoms do not oscillate in a simple manner about their equilibrium position. In the end some of the effects from an initial "perfect" wave will end up in all sorts of directions within the medium, with different polarizations. In practice there will always be chaotic behaviour among such a large number of atoms.

But I know little about material science, so maybe someone else will chime in with some "real world" knowledge.

There is a theoretical medium that is described infinitesimally as a chain of atoms with ideal springs between them. And possibly something like it for 2d and 3d.

The vacuum and electromagnetic waves is a good example, but that ain't a medium...

Torquil

 

[inflector]

Thanks Torquil,

In what sense do you mean that the forces that act between not act harmonically? I'm not sure what "harmonic" means in that context.

Can I assume that vacuum acts as if it is such a perfect medium even though it isn't a medium? Therefore that a perfect medium would act that way i.e. that vacuum acts like a connection of infinitesimal particles interconnected by infinitesimal ideal springs in three dimensions with respect to the propagation of electromagnetic waves (even though we know there's no medium there)?

- Curtis

 

[torquil]

Thanks Torquil,

In what sense do you mean that the forces that act between not act harmonically? I'm not sure what "harmonic" means in that context.

I may be the case that I misused the term. I meant that the potential well that each atom is located within is not a simple x^2 shape like it would be with the ideal springs. It would be a good approx. though for very small fluctuations, so I guess in the limit of a weak wave it would not be a problem.

Can I assume that vacuum acts as if it is such a perfect medium even though it isn't a medium? Therefore that a perfect medium would act that way i.e. that vacuum acts like a connection of infinitesimal particles interconnected by infinitesimal ideal springs in three dimensions with respect to the propagation of electromagnetic waves (even though we know there's no medium there)?

Yes I think so.

 

[Andy Resnick]

<snip>

Is there an ideal theoretical medium in which it is possible to propagate waves in an entirely directional i.e. straight-line manner so that the energy could be picked up at the other end of the medium? What would the properties of this ideal medium have to be?
<snip>

All waves diffract. The only oddball case I can think of are "bessel beams"

www.st-andrews.ac.uk/~opttrap/atomtrap/papers/Bessel_CP.pdf[/URL]

But those involve a singularity in the wavefront; I don't think an elastic wave can support such a singularity.

 

[inflector]

All wave diffract, yes, but don't they have to hit a surface of some dissimilar substance before this diffraction occurs?

Light, for example, diffracts when it passes through slits but not in a vacuum without slits. Right?

 

[Andy Resnick]

I'm not sure what you mean- I suppose if you had a point source isotropically radiating, the wavefront propagates without diffraction. But such a configuration does not ever occur, except in a limit: distant stars, (possibly) a single fluorescent molecule, etc.