Max. sound wave frequency (in solids)?

[NBerg]

I know, theoretically ultrasound has no upper limit (everything above 20kHz).. However, I was wondering whether on a practical note a maximum exists? I read somewhere that frequencies of the order 10^12 Hz were reached. Would a maximum frequency be based on the mean free path between the particles of a matter? Is there a direct relation with material density, i.e. more dense - smaller wavelength possible - higher frequency?

 

[nasu]

There are theoretical limits too. They are indeed related to the lattice spacing.
You can look up "phonon dispersion" for more details.
The sound waves will be associated with the so called "acoustic modes" of phonons.

 

[NBerg]

Alrigh, that is good information! Thanks,

I also found this:
"There is a minimum possible wavelength, given by twice the equilibrium separation a between atoms. As we shall see in the following sections, any wavelength shorter than this can be mapped onto a wavelength longer than 2a, due to the periodicity of the lattice."

I imagine smaller wavelengths suffer from more attenuation from material imperfections and grain boundaries, etc?!

 

[nasu]

Alrigh, that is good information! Thanks,

I also found this:
"There is a minimum possible wavelength, given by twice the equilibrium separation a between atoms. As we shall see in the following sections, any wavelength shorter than this can be mapped onto a wavelength longer than 2a, due to the periodicity of the lattice."

I imagine smaller wavelengths suffer from more attenuation from material imperfections and grain boundaries, etc?!

Not really. As you quote says, shorter wavelengths are physically identical with some longer wavelength. That means the configuration of the system will look the same. You may find a graphical illustration of this in the book you are using.
It is a property of a pure ideal crystal. Nothing to do with imperfections or impurities.

 

[NBerg]

Well yeah, a single crystal would be ideal for sound propagation. But what if these crystal-generated waves are transferred to other, less ideal materials?
The quote says 2a is the smallest wavelength possible. Larger wavelength (modes) do exist though. Aren't those less susceptible to disturbances? It's frequently said that low pitch sounds travel further than high pitch ones right?

 

[nasu]

OK, now you are talking about a somehow different aspect.
The minimum wavelength is due to the discrete (atomic) nature of crystals. In a continuous medium (this is an ideal concept) there will be no minimum wavelength.

The attenuation of waves (of any kind) depends on the quality of the crystal, defects, impurities, etc. The effect of each factor depends on wavelength.
For ultrasound there is indeed a tendency for attenuation to increase with frequency, at least for many common media (water, metals, biological tissues, plastics).

 

[Dickfore]

In the http://scienceworld.wolfram.com/physics/DebyeTheory.html" .

 

[NBerg]

Alright, thanks for the clear explanations! This was very helpful! :)