I am studying Debye theory of Specific heat.
hyperphysics has this picture and there it says
"Considering a solid to be a periodic array of mass points, there are constraints on both the minimum and maximum wavelength associated with a vibrational mode.
By associating a phonon energy
$h\nu = \frac{hv_s}{ \lambda} = \frac{hv_sn}{2L}$
with the modes and summing over the modes, Debye was able to find an expression for the energy as a function of temperature and derive an expression for the specific heat of the solid."
on Wikipedia there is this image saying "Consider an illustration of a transverse phonon below."
From these two images it seems to me that a solid modeled as a chain of point masses can have different normal vibrational modes. And any combination of these vibrational modes could also be possible.
My first question is that does all these normal modes of vibrations are phonons and any combination of these normal modes of vibrations is also a phonon?
My second question is related to the calculation of internal energy of the solid. In Debye theory they are calculating average energy of a mode and multiplying that by total number of modes to get the internal energy of the solid.
Suppose we have a solid modeled as a chain of point masses. Than this solid can have different vibrational modes as shown in these figures.
My question is that at any time are all these normal modes are present simultaneously in this solid (modeled as a chain of point masses) and i.e. why we are multiplying average energy of a vibrational mode to the total number of modes to get the internal energy of the solid?
