"Ability to transmit" is a bit vague. In any material, a wave will
encounter attenuation, an impedance, and a velocity, all of which are
determined by material properties of permeability, permittivity, and
loss tangent. The change in impedance from free air causes reflections,
and the change in velocity causes refraction. If your main concern is
attenuation, it'll be negligible for the styrofoam at that frequency. If
you're interested in calculating precise values or investigating other
materials, a good reference is Kraus's _Electromagnetics_.

Roy Lewallen, W7EL

David Harper wrote:

I was wondering what the general relationship between frequency and
its ability to transmit through various materials? For instance, 1GHz
and 1MHz obviously transmit differently through materials. I'm
curious as to what material properties are involved (i.e. dielectric
constant, density, etc?)

The main reason for this questions is I'm wondering how well 1+ GHz
(GPS) signals transmit through about 1.5 inches of expanded
polystyrene (styrofoam).

Thanks in advance for any insight!
Dave