1. What exactly do you call a wave similar to the Scope Visualization in WMP? I've been calling it a Vox wave, but I have a feeling this isn't right.
You're right it isn't right
Either you call it an oscilloscope trace, an instantaneous voltage display (a bit "artsy" though), or an amplitude/time display (If you are a 5th grade physics teacher).
If you wanna describe just the waves shown, it can be just about any waveform, but any waveform is a sum of sine waves of different frequencies (except a pure sine, which is only one frequency but cannot be found outside a lab or similar controlled environment).
[...] I've got some idea to make a circuit that could duplicate it onto a screen of some sort.
2 What are your ideas for a circuit that could take a sound wave from say, a iPod headphone jack, and create visualizations on a screen. I suspect you use a circuit that sends different voltages or waves down different pathways, which are then displayed in columns on a screen.
Oh well, you should fully explore your own ides before asking for other peoples same.
But here's a hint... It's called an oscilloscope and you don't need to reinvent the wheel, just buy an old 'scope and hook it up.
One (1) voltage send through one (1) "pathway" and displayed as one (1) trace.
A fast timebase, persistence of the eye (and of the phosphor coating on a 'scope) is what makes it look like several traces.
3. What sort of screen would function best with this circuit? A computer monitor? A large LED array? I have a feeling the LED array would be easier.
The 'scope allready comes equipped with a screen.
If you really wanna make an inferior circuit, an LM3915 in dot-mode can be multiplexed onto eg. 10 columns of 10 LEDs, to create a very low resolution 'scope.
If you google "LED Oscilloscope" you'll get tons of circuits, all of them probably with LM3914, as this is linear, but for sound, the logarithmic LM3915 is better suited (same pinout, so they can use the same PCB).
Good resolution and fairly simple construction can be done with a LASER module, a motor with a speed regulator made for the purpose, 6 or 8 small mirrors, a small worn out speaker, a piece of rubber "foil" or similar and a small amplifier made for the purpose. The "screen" is whatever you point the output at.
(Way before LASERS, we used regular lamps and lenses to get a small dot of light).
Anyways, I don't think I'll build this until I have money, so all I really need are theories, though any DIY projects with similar ideas would be nice. Thanks for the help!
You won't need that much money. You could get an old oscilloscope for perhaps $20 (since it don't need to be in any particular shape besides being able to show a trace). 100 LEDs, an LM3915 an op-amp and some "glue" is not particular expensive and the LASER version needs eg. a cheap LASER pointer, besides what you can probably mostly get from a dumpster (old VHS recorders have motors and stuff) and a glazier (if that's the right name, will probably give you the small pieces of mirror you need for free, as he bins much larger pieces regularly.