Observer and all, I am sorry for not reading through the entire tread, I wanted to at the beginning but its just too much so I jumped to the last posts. So if any similar points have already been brought up and proved/disproved, then again, I'm sorry
Now, this is just in line with what I have tried to understand for so long, steadily finding out that there is much that I didn't know or was wrong about. I had similar discussions with hansvoliven and fritz in regards to explaining the perceived increase in both amplitude and duration of the emitted sound with and without a resonator. In the end it boiled down to impedance matching, which frankly was a topic I was to inexperienced in to respond, so it stayed at that.
Now however, with gained insight from many other similar systems, based on forced oscillation and resonance, I believe I understand how it all connects, and why impedance matching alone cannot explain the phenomena of increased amplitude output from a resonantly driven oscillator.
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So first to impedance matching.
It is crucial in the construction of a system where you want energy to be transferred through several oscillators and eventually to a load. For example in audio, transformers was used to step down the voltage so that the impedance of an eventual speaker would "seem" higher to the original source, thus causing more of the voltage drop to stay over the speaker coils instead of any resistive load elsewhere. Doing the opposite over long range power lines, the impedance of the long thin cables seemed smaller than the final destination, even if both where of the impedance without the transformer.
So this is important if we want to transmit the vibrations of a string to the air around it.
If the want the main resistance or opposition to change to be the air, and not friction or other losses, then it needs to have a larger resistance than anything else in the "circuit".
And, theoretically it can only reach a 100% efficient transfer.
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Other attempted explanations has been that the sound is focused or that some inaudible frequencies are being limited and turned into audible ones. Both of these can be proved wrong in simple experiments where a pure sine wave is used and a very directional cone is pointing away from you.
The results are (and I have tested them) that the sound is still magnified by a very large amount, and that the direction which the cone is pointing doesn't matter the most as to how high the volume is. The equipment used was a small horn, a very small speaker (the ones you can place in the ear) and a computer program which can create sine waves and others at specific frequencies.
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Now in my attempt to explain why this and much better controlled experiments would still show a big gain in the output amplitude, I see it as a completely basic result of the phenomena of resonance.
The implications are gigantic, if we can try to get our heads around the problems and results of resonance.
As a prerequisite in order to understand this better (at least for me), it is useful to investigate the function of the 2-stage oscillator, and the concept it uses. If you have done this, you will come to see that it is in fact exactly the same as an acoustic resonator, only that the vibration frequency is much lower, and instead of air resistance it uses a mechanical load.
Both resonators are exited by a small trigger signal, resulting in a new signal who's amplitude is directly proportional to the Q of the resonator times the input power.
As people working with LC circuits (tanks) know, resistive resistance in the circuit will lower the Q, minimize the oscillating energy and offer no way to exploit the huge increase in amplitude which the tank gives.
Looking at it in the acoustic wave way, the problem is that you are trying to tap the energy from the anti-node. The exactly same problem arises with springs and weights, pendulums, air pressure, and even standing sound waves. And here lies also the key:
You want to tap it at the node, at the point which the wave reflects and cause a standing wave to arise, where the motion is at a minimum, or zero if there truly existed real nodes in oscillators.
The losses you get from tapping it here is of a completely different kind than the ones you have between the nodes.
Consider an attached spring with a weight.
You steadily input energy in the form a push on the weight at the resonant frequency.
In short time the amplitude may be twice or even ten times as high as your input, but, it you then switches the input into an output by placing a physical resistance close to it (a liquid), than you will get exactly the same out as you placed inside. The losses was proportional to the velocity/amplitude and you ended up with nothing.
Now take the same spring and weight, but attach the spring itself to a load, a friction element maybe, for consistent results. What in the world has happened?
What has happened is that the losses are no longer proportional with the velocity/amplitude, but only to the displacement of the spring.
When work is done in the load, the spring moves, and the weight looses potential energy as a result. This loss is proportional to the distance the spring moves. No matter what amplitude it is running in, the losses stays the same, as long as the distance is the same.
This means that the positive work done on the resistive element is not equal to the negative work done in the oscillator, because the value of force can be whatever we want without effecting the oscillator.
I apologize for the long and maybe untidy writing, I'm not that good at writing concrete and short, but in my view this translates to all other oscillators.
If the energy input is constant, and we vary the node resistance, then the amplitude of the oscillator will be proportional to this resistance. Energy output will then be: E(out) = E(in) * R(node)
And COP would be the same except /E(in) at the end.
See, the Q controls the amplitude and is equal to R(node) - R(anitnode)
So if we want to create as an efficient oscillator as possible, then the resistance at the anti nodes (air resistance, friction and others) needs to be as small as possible, while the resistance at the nodes needs to be as high as possible, and this would be our load.
In a LC tank the load should be either in the magnetic field or in the electric field.
The rotoverter is an example of the former.
Back to the subject, in this case the load would be the air, in which we create sound waves.
A load in the anti-node would have meant that we first vibrated a string, and then used friction directly on the string to load it. I think this is why strings with higher frequencies are faster drained, because they meet a larger resistance against the air than the lower frequencies, like ac versus coils.
Also if we placed something that could absorb sound waves inside the guitar, then we would loose a lot more of the volume, not only because it is absorbed as heat inside, but because we restrict the input energy from creating standing waves, which in turn vibrate the lighter and looser top wood, giving us that extra free source of sound.
Thank you for your attention
Julian
