# Phonon and dispersion relation

hello im new in this forum.. and i would like to ask
first this is statement that i confused about
'At low values of k (i.e. long wavelengths), the dispersion relation is almost linear, and the speed of sound is approximately ω a, independent of the phonon frequency. As a result, packets of phonons with different (but long) wavelengths can propagate for large distances across the lattice without breaking apart. This is the reason that sound propagates through solids without significant distortion. This behavior fails at large values of k, i.e. short wavelengths, due to the microscopic details of the lattice.'

what is consider as 'long wavelength'? im a bit confused with ultrasonic testing which is used short wavelength but still can propagates through material for large distance..

and how bout thermal energy? are this also consider as phonon at short wavelength? because i could see that there are exist mode in debye model.. so i assume that it is phonon but different energy from sound..

but i read that phonon is speed of sound in lattice.. thermal and sound doesn't seem similar to me..

im sorry, im noob.. :'(

## Answers and Replies

Generally speaking if the wavelength is 10x the lattice spacing or more you can call it long.

Just because dispersion is high and wavelength is short that doesn't mean it won't propagate a long distance. You need high absorption and or scattering to attenuate the propagation.

can i say that photon wavelength are comparable to atomic spacing so it will only interact deeper in atom
and phonon wavelength is comparable to lattice spacing so it will interact with lattice not deeper than that?

and last question, is like statement below,
'As a result, packets of phonons with different (but long) wavelengths can propagate for large distances across the lattice without breaking apart. This is the reason that sound propagates through solids without significant distortion.'

can a phonon breaking lattice apart? can you give me any example?

thanks a lot for helping me :)