I'm also not an expert but this is somewhat along my interests so maybe I can add a little.
Rainbow's pond visualisation and explanations are great. Maybe except that the thing can work over wider frequency range.
Essentially the bigger the room (or an accustic cavity enclosed between the headphone plate and the ear canal), the lower is its 1st resonant frequency.
For example a room with a length of 3.3m (10ft) would have its 1st resonance near 45 Hz (or 2700 rpm).
Freq_of_resonance = Speed_of_sound / (2 * Length)
For the purposes of active noise reduction, this is the frequency below which the simple ANR concept of creating opposite phase but equal amplitude waves will work evenly across the entire room.
Below the resonant frequency, all tones are essentially at the same phase across the room. The cancelling signal also fills the room with uniform phase and the two combine to produce quiet.
Approaching the resonance and above it, the sound is found at different phases throughout the room.
Since the cancelling wave is produced at a physically different spot than the noise, you will end up with the picture of multiple wave rings in the pond, with some spots where they combine and some spots where they cancel.
To make ANR work in an aircraft cabin (or a car), a few things can be done.
If the cabin is small relative to the expected noise (propellers are #1 culprit in twins), you could get away with a single mike and a single cancelling speaker. You have to make sure that the mike pickup is filtered out above the cabin resonant frequency. This will prevent the system from even trying to work where it can't.
If the cabin is larger, you will need "local area" mikes. With pilots, you have naturally co-located mikes to take advantage of. In one aftermarket car installation, I think that they hid the mike in the headrest (it used car's stereo for its speaker and worked well for the driver only, I was told).
Then, you have to use "local area" directional speakers, perhaps pointed across the cabin (for shorter dimension), plus some accustic padding to make sure that the cancelling sound doesn't reflect and spread to other "local areas". Overhead (P/A style) speakers would be my first try.
More sophisticated directional speakers could use speaker arrays.
Anyhow, it's not easy but it can be done. If (big if) you have the development budget, time, and excess payload capacity to get rid off.
I think that the biggest challenge would be in avoiding heavy accustic padding and dividers. Oh yes, and the boom-box.
Javelin: Did anyone say anything why the system was only used during the cruise? (props kept out of sync in climb, power conservation, general mistrust?)
bm
PS: Disclaimer: I have never built such a thing. It's all theories and for all I know the world IS flat.