So what happens from the time the guitarist picks strings to the time the sound comes out the amplifiers?
Problem number 1 is that we don't know how to amplify sound waves directly in a way that permits much control. So we must convert the vibration into something that can be controlled more readily. The obvious choice is an electric signal, if only because it is the most easily manipulated, several phenomena can be used, and transducers are readily available.
So what's a transducer? For our purposes it's a device to convert one type of signal to another. Microphones, speakers, light meters in cameras, speedometers and countless other devices have or are transducers.
I already mentioned a transducer that could be used for the guitar - a microphone. But look around and you'll rarely see it. The problem is that they can pick up a lot of things besides guitar strings, leading to noise. To avoid this, we want something with "tunnel vision".
OK, we can measure other things about the string that aren't likely to be influenced by other signals. They are simple, but in fact their lengths, displacements, and tensions are varying in time with the vibration. We have we have common types of transducers for all of them.
The length could be measured dynamically in various ways. An electrically conductive string's resistance would vary over a narrow range, but that means you need a power source inside the guitar to power the ohmmeter. If the string could function as a fiber optic cable, the relative phase angles of the light transmitted and received could be used to measure the length changes. I suspect that all would pose amplification problems too - each string might need its own electronics to make sure that their signals all had the same relative strengths. Give me the money and I'll cook something up for you, but in fact to my knowledge neither of those offers enough additional benefits to justify the added costs and inconveniences.
How about the varying tension? For this we have piezoelectric devices, which respond to pressure changes. The resulting signals are unlikely to be contaminated with extraneous data. They may need a bit of cleanup and reinforcement first, but then they can be sent to the amplifiers.
The last alternative is the varying position or displacement. For this again we could use optical or other phenomena to measure, but in practice what has been most practical is to use magnetic pickups. This limits the materials we can use for our strings, and some would prefer materials that won't work such as gut or nylon. But it so happens that the materials we can use, such as steel, have virtues of their own, and if you go to buy strings the steel ones are far easier to find.
A typical magnetic pickup consists of a set of small permanent magnets wrapped in wire and connected together. Accordingly they impose a magnetic field on the surroundings. As the strings vibrate within that field, they cause the field to vary in the vicinity of the wires wrapped around them. When you vary a magnetic field in a conductor, you induce voltages in the conductors. These tiny voltages are sent to the amplifier for reinforcement.
Given that the magnetic pickups sense the relative motion of the guitar and the strings, and they are intended to measure the motion of the strings, it is important that they are rigidly mounted to a stable base. Otherwise you're also measuring the vibration of the guitar body too. This is especially important at high volumes, or else feedback can be uncontrollable. So guys who play loud, with exceptions like Ted Nugent (who else?), generally play guitars with solid bodies.
Terrific, we have a signal that varies with the frequency and the power of the input. But we're not through yet - hook this straight to a speaker and you'll get jack squat. What you need is more power. And Joe Schmoe on the street can guess that that calls for amplifiers.
Alright, this is long enough for now. It was going to be about all of the electronics at first, but it kept growing even faster than this sentence. Stay tuned for more boundless excitement as we venture into the wonderful world of Amplification! and Strings!