I have a 15mm copper pipe feeding a cold water tank which is very noisy after flushing the wc and using the shower.
I have clipped the pipe which vibrated alarmingly, this has helped but the noise still persists. I wonder if it may have something to do with the float valve in the cold water tank?
It is definitely the valve. As the valve wears, and the rubber seal becomes hard, the flow of water causes the mechanism to oscillate as you describe. It is a common problem. You have to put up with it, or replace the whole ball valve.
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