I have a faucet that makes a vibrating noise when turned on more than half way. It is the bathroom faucet COLD side. It does not make a hammering sound when turned off, only when it is turned on to mid or full. It is the faucet closest to the water heater and does not happen e to other faucets. Now I just replaced the WH and was hoping when I purged the air it would go away but it is still there. This noise before and after the water heater was replaced. I was hoping someone could give me some advice.

I believe the faucet washer has come loose. Shut cold water off and remove handle and then remove the stem assembly... most two handles are obvious... Then check washer on bottom. You may need to replace. Good luck.