﻿ Ring of Fire

## Ring of Fire

### de Broglie wavelength - particle/wave duality - Bohr atom

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 (p type of tubing) 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 (p speaker specs) speaker mounted 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 anti-node. Table 1 lists the frequencies corresponding to the first few harmonics. Note that these are starting frequencies for gas at room temperature. As the ring gets hotter, the resonant frequencies will rise.

table 1. Standing wave harmonics

p table for good frequency values

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 down it 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.