Sorry to be a jackass, but I have to address this point.
Dr. Bose may or may not be a smart guy and accomplished acoustician; however, I think it’s incorrect to give him much, if any, credit for inventing active noise control technology. As a partial cite, I offer the following quote:
“Where two condensations are added we obtain increased condensation, where two rarefactions are added we have increased rarefaction; while a concurrence of condensation and rarefaction mutually, in whole or in part, destroy or neutralise each other.”
From: Helmholtz, Hermann. On the Sensations of Tone. Originally published 1885. Page 28 in 1954 Dover edition.
Also, see the very informative “Active Noise Control FAQ” at http://users.erols.com/ruckman/ancfaq.htm
which includes the following reference and comment:
Lueg, P., “Process of silencing sound oscillation,” U.S. Patent No. 2 043 416, 1936. Generally considered the first published work on the subject, although Lueg’s German patent application predates it by a few weeks.
Finally, the key points have been correctly identified in the previous posts, I think. An active noise control system must be able to predict the sound that’s coming up in the future so that it can generate the appropriate out-of-phase canceling signal. Thus, an active noise system works well on repeatable noises, such as bladepass tones in fans, jet engines, HVAC systems, etc. Another successful (though not yet commercial) application is as part of an engine muffler, where the exhaust pulses can be predicted with some accuracy.
The corollary is that random, one-off, noises, such as conversation, gunshots, etc. can’t be attenuated, except to the extent that the headset acts as a regular earmuff.