Earlier this week I wrote up a brief outline of an experiment to measure the speed of sound using only your singing talent. I’d like to be able to do the same thing with the speed of light. But it’s a lot harder because light is so friggin fast. As with sound, the speed of a traveling wave c is equal to the product of the wavelength and frequency. If you can find both of those you can find c. Or you could do something like directly measure the time it takes light to travel a specific distance. This is what the early experiments done by Galileo and others attempted without success.
Today it’s doable with pulsed lasers and a decent oscilloscope. I’ve done it myself as an undergrad – bounce a beam of light down the hall and back and divide the distance by the time required to make the trip – a few dozen nanoseconds, generally. But while this is “easy”, it’s not cheap.
But earlier scientists managed it without that technology by carefully measuring the timing of the orbits of Jupiter’s moons. They also pulled it off by doing something similar to the laser pulse measurement where the pulses were both generated and measured with rapidly rotating gear teeth. But that’s neither easy nor cheap, not least of which is because the path required is still kilometers long under the best of circumstances.
So I have no good ideas that don’t involve cheating by assuming prior knowledge of physical information that we can’t measure ourselves. There’s a number of possibilities involving the microwave radiation put out by a microwave oven, but there I’m afraid I think it’s cheating to accept the 2.4 GHz frequency without being able to measure it.
But if you do, you can set rough limits on the speed of light by measuring the size of the microwave oven. The wavelength has to be smaller than the oven itself (maybe 40 cm?) and larger than the holes on the protection screen in the door (maybe 2mm or so). Multiplying those by 2.4 GHz gives an upper limit on c of 960,000,000 m/s and a lower limit of 4,800,000 m/s. Not great, but it’s a start. You could be more precise by measuring the wavelength directly by measuring the distances between hot and cold nodes on microwaved objects.