Does the amplitude/power of the frequency have to be taken into account when creating a faraday cage? Why do some microwaves still escape through a microwave oven? If one has a complete and metallic screen around a 10sq foot space, and that screen’s holes are no larger than the smallest wavelength (X) one is protecting the 10sq foot space from, then wouldn’t that 10sq foot space get zero electromagnetic waves in the spectrum of wavelength X and lower wavelength frequencies?

No, the holes don’t block the radiation, it merely attenuates it by an amount related to the hole dimensions and the wavelength of the radiation–specifically the ratio of the one to the other. If you want complete blockage, you need a solid wall. If the holes are much larger than about 1/10th the wavelength, the Faraday cage becomes almost entirely transparent to the radiation.

How do you determine the level of attentuation? How does this relate to the thickness of the material used to make the faraday cage?

The attenuation in dB (this figure is called SE, or shielding effectiveness) is calculated by 20log(lambda/2d) where lambda is the wavelength and d is the hole major diameter. Thickness is noncritical for suppression of the electric field component; only the hole major diameter matters.

No, thickness is important. An arbitrarily thin conducting sheet becomes transparent for one of the polarizations (TM Pol, i.e. the electric field normal to the plane of the surface) as the angle of incidence approaches grazing.

Also, wouldn’t the thickness of the cage material affect how much power it could absorb before excessive heating causes structural problems?

If you got thin enough, for any real material.

Actually, I came here to partially retract my statement above. It’s correct for nonmagnetic metals, like aluminum or copper. Steel has a large permeability, so if the screen is made from steel, it can be reflective approaching grazing, from interactions with the magnetic field.

So duct-tape cage (duct-tape contains little metal wires) would be just as effective as a cage made of 1/4" steel netting (given that they holes in both cages are the same)?

I’ve been using duct, or duck whichever you prefer, for more years than i care to remember and have never seen any with wires in the construction. Threads, yes, wires, no. I’ll have to have some proof of this one. In other words, “cite”.

A duct tape cage is damned near useless. As far as I know, gardebn-variety duct tape contains no metal wires. You’d have to really prove it to me. I do know it’s pretty useless as electrical shielding.

I put together two Faraday cages this year and refurbished a third. The density of conducting wires is pretty heavy in a useful faraday cage material – you KNOW the metal’s in there. Moreover, unless the coverage and closure is perfect, your caghe will still leak like a sieve. I spent a lot of time repairing rips in double-walled Faraday cages. Even with a door having spring-clip edges, I still got plenty of leakage unless the door was tightly shut and the clasp engaged. Feedthroughs were great sources of leakage unless they were quite deep compared to diameter.