Interestingly, around the same time that the tank started making the noise there was noticeable air coming out of faucets, like a burst of air when you would first turn one on. This was in the late summer, when it was hot. After a couple of months it was less and less air. Gradually, as it got colder and colder it never had the air problem. Not sure if heat/cold has anything to do with current problem. The banging sounds used to be a lot louder and frequent, too. We get pretty cold in the winter and somewhat hot in the summer. (slightly southeast of Denver metro)
Yes, it makes the banging sound inside the pressure tank a couple minutes when a water source is turned off; i.e. toilet flush, sink faucet off, outside water valve turned off.
Let me know if you need more photos or close-ups. Thanks! House built in 1974/75. We're owners since 2014.