In my lecture it says that the Debye frequency is the cutoff frequency. So is this also the highest phonon frequency? And if not, what is the difference?
A little background: I do have an exercise where I should say what the debye frequency of a monoatomic, cubic material with lattice constant $a$ and sound velocity $c$ is. I thought this is $$\omega_D^3 = \frac{6\pi}{a^3}\cdot v^3.$$ But in my exercise there is also given the highest phonon frequency $\omega$. So I wonder if there is a difference between those two things: debye frequency and highest phonon frequency.