Does Debye model have free fitting parameters?

Physics Q&A
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Question 5 of warm-up of today’s seminar reads:
The Einstein model has a material-dependent frequency \omega_0=k_BT_E/\hbar of the quantum harmonic oscillators as a free fitting parameter. What is the material-dependent parameter that plays a similar role in the Debye model?

The book, however, states:
[…] It should be emphasized that the Debye theory makes predictions without any free parameters, as compared to the Einstein theory which had the unknown Einstein frequency ω as a free fitting parameter.

I assume the question wants us to answer \omega_D as a similar parameter. However, why would we choose to fit it to a graph, if we can calculate it explicitly from \omega_D^3 = 6\pi^2 nv_s^3? (If I understood correctly, this is the reason the book states there are no free parameters).

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That’s correct. \omega_D plays a similar role to \omega_0.

The book is also correct: \omega_D depends on material parameters that are directly measurable: the speed of sound and atomic density. This is different from \omega_0, that we wouldn’t know how to determine.

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