Well, you sort of could use a static MP3, as long as you had some way of adjusting the phase - i.e. pause/unpause it for a moment, randomly till you get it to match.

That will work for an absolutely rigidly pure sine wave of identical frequency, and even then produces a cancellation moire pattern like this: http://en.wikipedia.org/wiki/File:Two-point-interference-rip... , not universal cancellation. Any frequency deviation whatsoever will produce something different. Trying to use this technique to "cancel" things that aren't sine waves and aren't even constant frequencies won't have any cancellation effect, it'll simply be two sounds instead of one.

(Record yourself saying something. Record yourself saying it again. Flip the phase of one of them and add them to each other. You can do this until the sun goes out, you'll never get a "cancellation", you'll just get two voices. A nice effect in some cases, it's one of my favorite things about 60s pop music even if it got overdone to the point of cliche, but not cancellation.)

Or, to say it another way, that won't work.

It is not possible to universally cancel one wave with another not in the same position. Noise-cancelling headphones work by, with great effort and with some fast processing, creating a small zone where frequencies human ears can hear are dampened to a significant degree where the eardrum is. This comes at the cost of making it louder in places where the ear drum isn't (which we don't care about), and IIRC at the cost of some very high frequency noise well above what we can hear (which we also don't care about). In a way, it's fair to say they barely work; not in the sense that they are poorly manufactured or anything, but that it takes great cleverness to get something that works even as well as they do. There's a reason why they only came to be very recently; it isn't anywhere near as easy as sticking a microphone on the outside, inverting the signal, and playing the inverted signal on a headphone speaker, which could have been done decades ago. That, too, will produce some exciting acoustic effects, but will only cancel a very small and effectively random suite of frequencies, and you won't find it useful in general. Noise cancellation is just shy of impossible, and only works with some heavy caveats, like having the cancellation equipment extremely proximal to the audio receiver (ears in our case).