What it shows:
In explaining the electron orbits in the Bohr atom, de Broglie's principle of particle wave duality allows you to treat the electrons as waves of wavelength nλ = 2πr where r is the radius of the orbit. Then the only orbits allowed are those which are integer wavelengths; in all other orbits the waves interfere destructively.
How it works:
The Ring of Fire is a length of Interlocking Metal Hose (galvanized steel) bent into a circle to form a torus. Where the ends come together, we inserted an inlet nozzle for the gas and two banana plug sockets to a 4" diameter woofer mounted snuggly inside the ring, facing down the pipe (figure 3). All joints are sealed with silicon rubber adhesive. The ring lays horizontally, and has holes drilled in its upper surface at equal intervals (figure 2). The ring is purged with propane gas which, when lit, produces a ring of small flames.
The speaker is connected to a signal generator 1 with sine wave output at 10V peak-to-peak. The standing wave set up inside the ring makes the flames grow that are under a high pressure anti-node and shrink under a low pressure node. As the ring gets hotter, the resonant frequencies will rise.
figures 1-3. The Ring of Fire
Setting it up:
Rest the ring on a lecture bench with part of it overhanging the edge (gas accumulates in the center if you don't). Purge the ring with propane for about five minutes with a reasonable flow, then turn it down to a trickle to keep it topped up. Light the holes like a birthday cake; the flames should be about half an inch high, so adjust the gas accordingly. There are three parameters to adjust for best results. Volume (signal generator amplitude), frequency and gas flow rate. Each resonant frequency will require slight re-adjustment. The flames can actually blow themselves out at some frequencies if adjustments aren't made, so practice beforehand.
The speed of sound in propane is 258 m/s. Thus, a frequency of 84 Hz would fit one wavelength into the circumference of the ring (=3.08 m). 168 Hz for two wavelengths, 251 Hz for three, 335 Hz for four, etc. Of course, as the ring gets hotter with time, the speed of sound will increase and these frequencies will drift. Also, note that a standing wave of λ gives you two maxima, 2λ four maxima, 3λ six maxima, etc.
A spectacular illustration of the old quantum mechanical theory of electron orbits.
1 Signal generator is an IEC F34 with 50Ω output