My kind of thread. hopefully it doesn't get jacked by bad info causing arguments.
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Can someone explain resonant frequency in laymen's terms really well and what affects it?
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I'm assuming you mean physical resonance, like strings, wood etc?
If you understand inertia, and springyness, you've pretty much got it. Push something in one direction against a spring and it will bounce back, go the other direction, bounce back, etc. The frequency of this resonance will be mainly decided by the mass of the object and the stiffness of the spring.
A heavier object, or a less stiff spring will lower the frequency, lighter object or stiffer spring will increase the frequency. if you try and vibrate it at a different frequency it will be easier or harder depending on how close your pushes allign with the speed and direction it's already moving. If you line up perfectly, it'll increase the size of the vibration. If are exactly opposite, you'll have to push harder, and will reduce the size of the vibration. In between will have an in-between effect.
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Can someone explain the physics behind the same string vibrates differently (give different sound) on different basses. I expect someone to talk about different thinsg like rigidity, some of the physics of how a string vibrates etc.
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There's an amazingly complex interaction between many different resonances, to the point where it can't be completely predicted (the reason arguments start) A vibrating string is the object described above. its spring is a combination of the stretchyness of the string itself, and the springyness of the neck, as the string tension slightly flexes and unflexes it each time it vibrates.
The next important effect is damping. Since springs aren't perfect (especially the parts made of wood) they don't exactly give back all of the energy exactly as it's given to them. some parts are absorbed (they actually turn to heat). as an example, you could make the spring of rubber instead of a metal coil. It'll still bounce, but will stop faster. Switch from rubber to foam, and it'll stop almost instantly.
when you introduce a vibration to the wood, its grains all act like millions of springs with different resonances which are pretty random, but are roughly grouped into certain ranges depending on the density/hardness in different directions in the wood.
This is what gives wood its "tone" for example. when you knock on it, you're giving it a whole mess of random frequencies. it absorbs some, while returning others (in varying amounts). hard and light woods should return most of their energy at higher frequencies, soft and heavy woods will return most of their frequency at low frequencies. Since most woods get harder and heavier at the same time, the frequencies aren't affected to quite the same degree, but what does change is the amount of damping. A hard, heavy wood will probably absorb less energy overall than a light soft one. All in all, it's really complicated, and mostly experimented with, giving relatively subjective measurements, and lots of room for excessive discussion/arguments.
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How about the way a pickup is wound? Low vs high impedance and why it's different.
I think the electronics is obvious but maybe someone could explain the way passive basses tone pot works? and why you get a certain sound when you mix both pickups together.
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To keep it simple, you could think of impedance as a combination of ordinary resitance, and two types of frequency specific resistance. Capacitive impedance is a resistance to low freqencies. The lower the frequency, the more resistance. Higher Frequency, less resistance. Inductive capacitance is the opposite. low resistance at low frequency, high resistance at high frequency.
Once you know that an inductor is usually a coil (like a pickup), this partially explains both of those questions.

A high impedance pickup (meaning inductance in this case) has a higher resistance at high frequencies, so it blocks more of the high frequencies than one with a lower impedance.
the tone control works by a combination of a capacitor and pot (which is a variable resistance) The capacitor will allow high frequencies to go through it while blocking low ones, but its function in a tone control is actually to reduce the amount of high frequency in the signal. It probably sounds a little backwards from what you would expect, since if you put a capacitor in the way of your signal, all that comes out is some high pitched squeaking.. all the low stuff gets blocked. The trick is that you don't put it in series with your circuit. You instead connect it to ground. What happens is it allows the really high freqencies through, Pretty much just syphoning them off into the drain to use the usual water analogy. of course, you might not want to dump quite that much of the high frequencies, so you put an adjustable resistor in there. The capacitor sorts the high frequencies out, and the resistor decides how much of them get dumped down the drain and how much stays in the circuit.
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I can actually explain this one a little bit but how about the placement of the pickup, or why the neck pickup sounds different from the bridge pickup though they are essentially the same physically.
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First thing to know is that all vibrations in the string are known as modes. they're the different ways that the string can vibrate, and they all line up perfectly with the ends of the vibrating part of the string. So, in the length of the string you can have 1 vibration, that takes up the whole length. (the middle of the string moves, and the ends stay still) You can have 2 vibrations (the wave has 2 bumps. The middle and each of the 2 ends stand still and the sections in between vibrate. 3 vibrations, 4 vibrations, same patern. I think you get it.
If you pick some different spots along the string, you'll notice that the further you are into the middle, the bigger the first mode (usually called the fundamenal) as you move towards the bridge, the less fundamental, and the more the higher modes will line up (though at a smaller and smaller total size the closer you get to the end)
So, the closer to the bridge, the more brightness and twang you'll get, the closer to the neck, the more of the bassier warmer tone you'll get.
What's kind of interresting is that the pickups are usually arranged to reverse this effect to some degree. The pickup that is put where there's mostly high frequencies, is the one that blocks more of the high frequencies. and the one with less high frequencies is the one that lets them through. This is probably since both of them do some of the midrange. if you put them in the opposite order you would end up with about the same midrange, but too much low bass and high treble. (This is just my guess though, I haven't actually tried installing them backwards. I might have to, just to satisfy my curiousity.)
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Well some of these can probably be broken out into different threads but I don't expect this thread to be terribly long as I hope it is not an argument on conjecture... I hope people would be able to back up what they said if it was needed.
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Hey, look. I made the thread terribly long all by my self.

Hopefully I explained it clearly enough that most people will get it.
And hopefully it's not so boring that nobody bothers to finish reading it.
-Nick