I was under the impression that, effectively, a speaker "sees" two potentials at its inputs: the ground wire and the "live" wire. I thought that basically an audio signal was produced by holding the ground wire at a constant, reference potential and swinging the potential of the "live" wire with respect to the ground wire, creating a different voltage drop across the speaker. Current then flows through the speaker according to Ohm's law, which drives the speaker and produces the pressure changes in the air surrounding the speaker that we perceive as sound. The job of an amplifier then is to increase the amplitude of these voltage swings, and thus increase the current at any given time pushing through the speaker, and make the sound louder.
If I am close to being right about that then I can't wrap my head around how balanced headphones work. I thought in the typical balanced setup, you have three wires for a specific reason. I thought that effectively you have 2 "live" wires who push the audio signal with respect to the reference ground wire, only they push the signal 180 degrees out of phase to each other. Then, once the signals reach the speaker, their is some kind of active circuit that puts the two signals back in phase with each other. Theoretically, both wires would pick up the same noise as the signal is "sent" to the speaker. However when the two signals are returned to being in phase with one another, the noise is now 180 degrees out of phase with itself. When both signals are then played through the speaker the two audio signals undergo constructive interference, effectively making the overall audio signal much stronger, while the noise undergoes destructive interference, effectively removing any noise that was generated in the cable.
How then does this work for balanced headphones? There is no ground reference for both signals, only and L+ and L- for the left channel, and similarly only R+ and R- for the right channel. Also, there is no active circuit that recombines the two out of phase signals. It seems to me that if there *was* a ground wire, with no active recombination of the signal and both feeding into the headphone driver, the signals would completely cancel each other out and you would only get the noise picked up in the cable.
I know that I have something really wrong in my analysis, but I can't figure out what, exactly. I would really appreciate someone with the know how explaining exactly what is going on at a headphone driver in both the single-ended and balanced cases.
Edit: I realized part of my problem in thinking about this is that I am basing my conclusions about the noise canceling for the balanced configuration on sine waves instead of the actual transient nature of audio. nevertheless I am still very confused on exactly what a balanced signal is and how it works to reduce noise, or even if I am thinking about how a single-ended device works properly.