I'm struggling to understand the relationship between the Debye temperature and the speed of sound in a substance. An example problem given is:
Estimate the Debye Temperature of Silicon and Lead, given that their respective speeds of sound are 9150 m/s and 1320 m/s. (not sure if its relevant to this part of the question but also given graph of C_v vs T for Argon from which you can read a Debye temp of about ~80K).
[tex]\Theta_D = \hbar \omega_D / k_b[/tex]
where [tex]\omega_D = c k_D[/tex]
and [tex]k_D[/tex] is the radius of the "Debye Sphere"
The Attempt at a Solution
Not sure how to attempt this to be honest, there seems like there are too many unknowns. Presumably there is some simplifying assumption, but I'm not sure where to begin...