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Tuesday, November 25, 2014

Albert Michelson’s Harmonic Analyzer

(5 short videos)

Albert Michelson (of Michelson and Morley fame) built this machine a hundred years ago. It can combine sine waves to produce complex wave forms, and with some fiddling, it can break down a complex wave form into it's components. Relative to sound waves it operates very slowly, but it illustrates the principles, and that was the important part, because back then not everybody believed that complex wave forms could be broken down into a selection of simple sine waves. Okay, not everyone believes it now, but as far as the religion of science goes, it is an established fact.
    It is a bit of a complex process, so even if the machine has no other practical purpose, it is a very good teaching tool. Nowadays computers can perform this analysis or synthesis in real time, think Moog Synthesizer.
    The fifth video in the playlist (there are five) illustrates the relative pace of the sign waves generated by the 20 levers in this machine. The cute part is that you can click on any of the numbered boxes across the bottom of the video and it will take you directly to that portion of the video. The last one, number 21, has all 20 running simultaneously, which is kind of entertaining.
   I was a little confused when I first started looking at this machine because all the gears appear to be straight cut gears, meaning that the shafts of two meshing gears should be parallel. This machine has 20 gears of graduated sizes, all on one shaft, meshing with 20 gears, all the same size, on a second shaft. If the shafts are parallel, the machine won't work because only the largest gears will engage. But you can't run them at an angle because that would be wrong! Only a neanderthal, or a heretic would attempt to mesh straight cut gears at an angle. But that's what he has done, pagan free thinker that he was. Of course, we are running this machine without any kind of load, it's only being turned by hand, and only intermittently, so I guess it will survive. And guess what? It has.
    He also built one with 80 gears.

This whole business of decomposing wave forms kind of bothers me. If you can do analysis with 20 gears, why do you need 80? Why do you even need 20? Shouldn't 2 be enough? I suppose it's a matter of how accurate you want to be, which is kind of contrary to all the mathematics I was taught, which was all about having the right answer, not some approximation thereof. Can you imagine what your teacher would say when she asked you how much two plus was, and you answered that it was approximately five?
    I guess approximations are the name of the game these days. Jack tells me that the wave forms that come out of analog equipment that are supposed to be clean and pure are not, and that digitally synthesized wave forms are usually closer to the ideal. Talk about faith in the unseen. What I have believed all these years turns out to only be an approximation of a theoretical construct. God forbid we could see what all the electromagnetic radiation going on around us is actually doing.


Ole Phat Stu said...

The analysis is a Fourier transform.
So the most you can get is not 2, or 20,or 80 but half of the highest frequency you are analysing for (c.f. Nyquist). Divide that by the bandwidth of the channels you are looking for and you'll get the number of channels.

If you are keen on using the number 2, then do the Fourier transform using Tukey's FFT algorithm.

Charles Pergiel said...

I knew that, once. Problem is I immediately go to the hard case: square waves, where if you want to be accurate you have to go to infinity, and everybody knows no things actually go to infinity, so we are stuck with an approximation. Never mind that nobody can make a perfect square wave. At least nobody I know. Maybe God, Michelson and Stu.