In an optics class I took in college one day the professor picked up a ruler and said "Let's measure the speed of light". The class laughed, and then he proceeded to measure the speed of light with his ruler.

It was a metal ruler with the distance markers raised. He put the ruler on a table, reflected a laser off the ruler onto the blackboard and got a diffraction pattern, marked the positions of the lines of the diffraction pattern with some chalk, marked the position of the ruler on the table, and then turned off the laser.

Then using the ruler he measured the distance from the mark on the table to the blackboard, and measured the spacing of the lines in the diffraction pattern. It was then a short bit of math later and he had the speed of light.

Of course he had to use the frequency of the laser in that calculation, and the frequency of the laser was almost certainly calculated using the speed of light so in all likelihood all his demonstration actually did was verify that the frequency of the laser was really what the manufacturer said it was.

That then raises the question of whether there is a way we can determine the frequency of visible light without knowing the speed of light.

We could do it for radio probably fairly easily by a method I'll describe below but I don't know if that could be pushed all the way to visible light. On the other radio might be good enough. A 2.4 GHz radio wave has a wavelength of around 12.5 cm. I'd guess that it would be practical to build something that could make a diffraction pattern with that and let you then calculate the speed of the wave just like my professor did, albeit you'd need a lot more room than we had in the lecture hall.

Here's how I'd go about trying to get a radio wave around 2.4 GHz without knowing the speed of light or using anything that depends on knowing the speed of light.

First, I'd build two variable electronic oscillators and adjust them to match the frequency of the D right above middle C on my piano. That's 293.665 HZ.

Then I'd tune one of the oscillators up until it is twice the frequency of the other. You can build circuits that can detect when one oscillator is twice the frequency of another. You can even use those to build feedback circuits to adjust the tuning of the second oscillator to keep it exactly twice the first if either drifts a little due to things such as temperature changed.

Then tune the first to be twice the second. Keep doing this. If you can do this enough to get 23 doublings you'll end up at 2.46 GHz.

You probably can't actually do that with the original two oscillators, at least if you start off with simple EE 101 circuits. You might have to build more sophisticated oscillators along the way.

Actually, it might be best to build 23 oscillators instead of swapping, so you can have the complete chain of frequency doublings available, with each oscillator locked to twice the frequency of a neighbor by a feedback circuit.

To extend this all the way to visible light you'd need 37 to 44 doublings, depending on which piano note you use as your reference.

37 halvings brings visible light down to 2900-5800 Hz. The notes F#7-C8, 2959.96-4186.01 Hz, (82-88 on the standard 88 key piano) are in that range. You can halve visible light up to 44 times and remain in piano range. 44 halvings bring you to 23-45 Hz. The notes A0-F1, 27.5-43, 6535 HZ, (keys 1-9) are in that.

I don't think we have nearly as much flexibility with light as we do with radio when it comes to making variable oscillators and with making things that can detect when one light source is a frequency that is an integer multiple of another, so I don't know if it this method could be extended far enough.