[qqii]

In reality noise cancelling headphones don't "just reverse the wave", since that's often not fast or accurate enough (too noisy). Instead it's more like:

mic -> fft -> secret suace analysis and filtering -> unfft -> speaker

A simple filtering would be a high pass filter, to avoid random high frequency sounds from constructively interfering producing more high frequency static.

Just a random tidbit, if you listen to rtings' examples or have a pair yourself I'd suggest playing some different colours of noise to see for yourself!