This comment is technically incorrect. Noise-cancelling headphones work the way OP described, and are limited to working in a cavity which is smaller than the

This comment is technically incorrect. Noise-cancelling headphones work the way OP described, and are limited to working in a cavity which is smaller than the wavelength. There are predictive noise cancelling systems too. These are commonly built into industrial equipment. You might, for example, have a fan or motor which spins at 5000 RPMs, and what do you know, it has a consistent noise profile on each of those rounds. If you cancel that noise profile, you do pretty well. These systems both reduce noise and extend equipment life by reducing vibration. They also work to higher frequencies (in part because speed-of-sound in metals is > 10x that in air, and what matters is wavelength more than frequency). There are ones which are open-loop used in HVAC systems. If I have a pipe, I can record sound on one end, and play a cancelling waveform on the other end, with an appropriate delay. I haven't followed the field, and when I looked, these were mostly expensive prototype systems (I'm not sure if they ever made it into mainstream use), but they did work. They needed to be calibrated for each HVAC, which made them impractical for most real-world applications. There are all sorts of ways to do active noise cancellation. Many of these could be implemented on airplanes. Most of these techniques were implemented decades ago, when computation was a lot more expensive. A simple feedback loop is a few opamps, capacitors, and inductors, so pretty cheap to toss into headphones with 1990's-era technology. One could do a lot more with teraflops....