What it shows:
The depth to which electromagnetic radiation can penetrate a conducting surface decreases as the conductivity and the oscillation frequency increase. This demo compares the skin depth of AM and FM radio frequencies, and shows just how small these distances are.
How it works:
An electromagnetic wave entering a conducting surface is damped and reduces in amplitude by a factor 1/e in a distance ∂ given by 1 
where ω is the angular frequency of the radiation and σ the electrical conductivity of the metal. This distance is referred to as the skin depth of the conductor. The effect is caused by electromagnetic induction in the metal which opposes the currents set up by the wave E-field, and holds for oscillations below about 1012 Hz.
The detector for the transmitted radiation is a small portable AM/FM radio. 2 To test the penetration of radio waves, the radio is placed inside a small (25x25x25 cm) cardboard box wrapped on five sides with aluminum foil. The sixth side (the lid) is covered with aluminized mylar with a thickness of 12.7μm.
Two suitable sources of electromagnetic radiation (in the Boston area at least) are WHDH at 680 kHz AM and KISS 108 at 108 MHz FM. For an aluminum surface with conductivity σ = 3.6x107 Ω-1 m-1, the skin depth for WHDH is 1x10-4 m, and for KISS 8x10-6 m. Consequently, the lower frequency AM oscillations penetrate the box and are detected by the radio receiver, but the higher frequency FM oscillations aren't.
Setting it up:
On the lecture bench. The lecturer tunes in the radio and places it inside the box. A piece of paper with the relevant station frequencies is a good idea.
Comments:
Turn up the volume really high, because the AM station suffers a lot of attenuation as well, and the audience at the back won't hear a difference.
1 G. Bekefi and A. H. Barrett, Electromagnetic Vibrations, Waves and Radiation, p.321 (MIT Press, 1977)
2 The cheaper radio the better, with no automatic gain. We use a Radio Shack AM/FM FunMate pocket radio.