I once programmed my TI-84 calculator to do exactly this! The only missing thing was a circuit to convert the audio jack output voltage into the needed form for an antenna. I had the CS know-how but no EE know-how, so I never got it to work. It was fun to dream about confusing my high school's clocks though. (Sadly, the other obstacle was that the clocks only listened for the signal overnight, which improved their chances of detecting the weak broadcast out of far-away Colorado.)
> audio jack
That's a serial port, except when you're playing Bad Apple
I didn't know that about the overnight; that's neat. I'm often in my garage before work, and I always assumed the 5am reset time was just because only weirdos are noticing a clock whir its arms around then.