A crystal radio is a common enough science fair project, but the problem is, there isn’t much on anymore. The answer is, of course, obvious: build your own AM transmitter, too. AM modulation isn’t that hard to do and [Science Buddies] has plans for how to build one with a canned oscillator and an audio transformer.
We don’t imagine the quality of this would be so good, but for a kid’s science project it might be worth a shot. Maybe something like “What kind of materials block radio waves?” would be a good project statement.
The site is aimed more at kids and has a good list of materials (mostly from Jameco). They do credit a site that has a more detailed explanation of how the thing works, though. Both sites have a lot of other projects that would be suitable for a young hacker’s science project.
If you look at the wiring, you’ll see that the transformer actually influences the power to the oscillator. This is a crude way of getting amplitude modulation, but it works. A better way is to let the oscillator run and modulate an amplifying stage as the signal goes to the antenna. However, this transmitter is low power and low fidelity, so the simple set up is more than adequate.