Assuming you want to cancel frequencies up to 1kHz, you're going to need mics every 30cm at least for a useful sound field. For a 787 fuselage, that's about 60 around by 190, let's round that down to 10000 microphones. But of course, then you need electronics for them, and a way to carry the signals back to somewhere for processing. That's about 10 Gbps of data, fine, doable, but then you need to process it. Since you need to cancel separately per passenger, that's 2.4 million filters (10k mics * 242 passengers) to process. Nevermind that since this is a plane, there is a huge amount of overhead due to safety requirements.
This is all assuming this whole idea works, which it probably won't, because it's not just about the microphones on the fuselage but also how sound is transmitted inside the plane and other noise sources.
That sounds reasonable. Let's do the math your way in both directions:
1) Assuming system-level model
10,000 microphones * 8 kilosamples per second = 800 megasamples per second.
NVidia Tesla does 100 teraflops. I get about 125,000 FLOPS per sample. That feels adequate to me!
2) One filter per microphone per passenger. We need to divide by 250.
500 FLOPS per sample per passenger. That's more than enough for a very fancy IIR.
Of the two, I think #1 is more likely to work than #2, precisely because you want a coherent model. If you want to adjust your model for someone walking down the aisle (or any kind of system ID), that's a lot easier with 125,000 FLOPS per sample than 500 FLOPS per sample.
Right, and now you've achieved the same noise cancelling performance... That off the shelf noise canceling headphones achieve (1 kHz) without putting 10000 microphones on the plane.
Again assuming this all works, which is a massive if.
.... in the same way that having a billion transistors in a computer isn't practical. Or a computer in every car tweaking fuel injection. It's not practical until it is. Electronics goes down in price. Algorithms improve. Insulation stays fixed or goes up in price. I would say it's not a question of "if" but "when."
The answer to that might be right now (we couldn't do it before, and we probably can today) or it might be in a decade. But electronics will keep falling in price. 10,000 microphones * $5 per microphone+electronics = $50k.
The advantages of cancelling an entire wavefront go well beyond passenger comfort too. Industrial noise cancelling systems are more about equipment life than about employee comfort. I had laptop screws unscrew on airplanes before, due to vibration. If planes need less maintenance as a result of active vibration reduction throughout the airplane, you'll make up that $50k virtually overnight.
As a footnote, the crazy part here isn't the 10,000 microphones, but the speaker-at-every-seat part. You'd almost certainly want both the microphones and speakers in the skin of the airplane. But that's a story for another day.
This is all assuming this whole idea works, which it probably won't, because it's not just about the microphones on the fuselage but also how sound is transmitted inside the plane and other noise sources.