Consider an attenuation coefficient $\mu(x,\omega)$ which depends on material (that is, on the space variable(s) $x$) and frequency variable $\omega$.
The attenuation can be of electromagnetic radiation or of sound, for example.
Is it reasonable to make the approximation $\mu(x,\omega) = \alpha(\omega)\beta(x)$, where $\alpha$ is independent of the material and $\beta$ is independent of the frequency?
Context: I have a nice proof for a physical model, the derivation of which requires making this factorization assumption. Thus, I am interested in how reasonable an assumption this is, and under which conditions it is reasonable.