This is a strange problem:

I recently noticed that when I turn off the water in my bathroom sink,
the "pipes" start banging. I can get the banging to stop by opening
the same bathroom faucet for a few seconds. When I do, the water
comes out in spurts, then evens out and the banging stops.

I've actually isolated it to this: When I turn off the water, there's
something that gives my toilet tank a little "jolt", (maybe a
vibrating pipe?), and the float arm starting vibrating, which is what
causes the banging.

I couldn't possibly be making this up.

This has not been easy to describe, and I'd be very grateful if anyone
has any thoughts on what I can do.

Thanks!