A great demonstration of standing waves

The Rubens Tube.
Get some pipe, drill regularly spaced holes down the length and connect it to a gas supply. Mount a loudspeaker at one end and seal the both ends (Gas leaks are not normally a good idea but it may add to the pyrotechnic effect!). Turn on the gas and light it. Now you have a nice fire. OK, now play a clean musical note through the speaker and tune it in to set up a standing wave in the tube.



How does it work? There's my explanation tucked below the belt.

Think first of a guitar string. It's fixed at each end but free to vibrate everywhere else. The deepest note is produced when the whole string moves in a smooth curve once per cycle like the top string in the image. This note is the fundamental and because the string has to move down and back up to return to its starting point, the wavelength of the note produced is twice the length of the string. Now as any guitarist knows there are places on the string where you can dampen the vibration with a finger to tease out the harmonics. This is not fretting the string by pressing it to the fingerboard, just gently touching. These spots are called nodes where the wave energy passes without causing movement. The ends are forced to be nodes as they simply cannot move but act to reflect the sound waves. You can see by counting that all possible harmonics can be produced by a string. Salford University has a primer on string vibration with good video and animations. I should point out that the tension and weight of the string affect the speed of its vibration and hence the note, but that's not so important for this explanation.

So what happens with a tube? Obviously it's not the tube which is vibrating but the air (or propane) inside it. In addition the ends of the tube can be open to the surrounding air (see warning above) or closed. Look at an open tube.
Unlike a string the air at the open ends is unconstrained and so cannot form a node. They must be antinodes. The first node then comes in the middle. Similar to a string however, the wavelength of this fundamental is twice the length of the tube and all harmonics can be produced. This is the basis for many musical instruments from the humble recorder to the mighty open organ pipe. The equivalents of tension and weight for a string are air pressure and density in a tube. Simplistically we can assume these to be constant otherwise it would make playing in an orchestra rather difficult.

What happens if you close one end? Confusingly this is referred to as a closed cylinder even though one end is still open! Anyway, at the closed end nothing can move. It's like the fixed end of a string, it forces a node. The open end can only be an antinode and this makes for some interesting properties. Firstly, the wavelength of the fundamental becomes four times the length of the tube. More interestingly, only odd numbered harmonics can be formed. This is what gives the haunting sound to instruments like the closed organ pipe, where they put a bung in the top, and the clarinet, which by clever design of the mouthpiece almost achieves a closed end.

What does closing both ends do? Make a sealed cylinder I guess. Not much use as a musical instrument unless you are going to hit it, you can't blow in it. It will still have resonances though, and the same as a string both ends are nodes. But hang on, you are driving one end of the Rubens tube with a vibrating membrane, the loudspeaker. If the speaker is moving backwards (causing low compression) in sync with an incoming high compression cycle of the sound wave they can cancel out - this gives a node. If the speaker is moving forwards (high compression) and again meets up with a high they will reinforce each other, just like an antinode. You can see this in the Rubens tube video above when they a going through fixed notes. The speaker is on the left.
Here it's a node:





And here it's an antinode:





So there you go, I just wonder what you could do with 50m of gas mains and a few kilowatts of bass guitar! Anyone got a JCB?