So, as we have discussed, we will only really be concentrating on 'swing resonance'. You could theoretically apply a white noise to a bell resonance, to get high volume, but it can't really happen because of the mechanism of the forcing function. In reality, the other frequencies get in the way, and damp down the input. An opera singer can shatter a glass, but involves pure tones, and fine interactions.
I actually have two forms of swing resonance. One is detached, intelligent tuning, such as a trumpet (and the swing!), and the other is 'mechanism tuning', where the source 'automatically' tunes through basic physics.
The most abused term I ever saw was 'organ pipe resonance', as though it was a bell resonance responding to white noise. This was one of my biggest battles regarding the flow resonance at Darlington, and I was roundly defeated, due to an unusual property of this type of resonance, which will be mentioned later. But I digress.
The organ pipe resonates a given frequency depending on its length. It is an open-end sonic resonance, which means the compression wave zooms down the pipe, meets the open end and reflects back. An open end means it starts as compression and reflects back tension (negative pressure). A closed end would mean it reflects back positive pressure (compression).
As can be imagined, this is no bell resonance, since there is nothing more inefficient than an open-end resonance. Makes it useful as an instrument, since all that inefficiency comes out as sound! The organ pipe makes a very loud sound, with apparently very little input. How does it do that?
It has a self-tuning source! The air stream comes in flat and is directed to a knife edge. If nothing was happening, it would split itself evenly on the edge, and no sound would ever come out. But it is not stable! The slightest disturbance causes a wave to zoom up the pipe and reflect back. The negative pressure wave sucks down the air stream into the pipe, which starts another compression wave. If we had our handy-dandy accelerometer, we would notice an explosive exponential. Very tiny waves suddenly blowing up into full sound, where non-linear damping stops the pipe from blowing up!
Now, getting back to electrical lines, which I think started this whole thing, they also have 'galloping' waves which can destroy the whole tower!
Therefore, they can have these cute little things (Stockbridge Damper), which work in weird and wonderful ways.
The power line wobbles in the wind, but if it is stretched tight like a guitar string, it wobbles at a steady frequency. The air acts as a non-linear self-tuning source because of aerodynamic effects. As the line moves perpendicular to the wind, it actually experiences a greater force pushing it, because of lift effects, much like a spinning curve ball. The whole effect becomes an organ pipe, and can grow to tremendous levels!
Those teeny little damper can actually work, if they nip the first tiny vibrations in the bud, before it starts to grow. That would be like having a very tiny damper in an organ pipe to kill the first leaders. If you measured with your accelerometer, you would see the first waves could not grow to an exponential monstrosity.
That's where Darlington was 'fixed'. They mucked with the system, and stopped the leader waves, by changing the pump. They declared it 'done', and walked away, and also installed some small dampers, equivalent to the power line version. They never saw the full physics, which is not important to an operator, but really important for the next version, which uses higher flows! Ah well, I have recovered.
To be continued.