I wasn't clear : phase shift has a clear example: think of two sine waves, one whose value at time t is sin(t) and the other sin(t+pi/2). they'd have the same period, and frequency, but would be phase shifted by that addition in the time parameter.
For another fun example, here's the residential power in current American homes: two 120v A/C feeds, out of phase so that you can combine them in the breaker box to get 240v A/C.
I’m aware of how ANC works. It uses the same frequencies with reverse amplitude. The comment you objected to however was talking about different frequencies.
Right? One of my dumb noobie questions has always been why textbooks explain ANC as "180 phase shift" instead of "reverse amplitude". Do they really do an entire DSP pass to break apart a signal and phase-shift it just to get the output that a minus sign could get? There must be something missing from the plum-pudding model.
It's only a sign flip when the detector and emitter are perfectly in phase. Adding delay causes the required phase shift will drift slightly. Also note that the phase offset of a delay is frequency dependent, so this drift will be as well.
Another reason is that devices and materials have different frequency responses, so an external signal needs to be filtered to match the levels in the device.
The key is that we can still analyze and manipulate frequency components independently in REAL PHYSICAL WORLD, which enables techniques like OFDM.