I have a mixer tap in our kitchen sink. When you close the cold valve, there is a bang from underneath the house. Tracing the banging, I can feel it from the mixer-tap pipe all the way through to the hot-water system (where the cold water inlet is). I can't feel it in any other pipes. All the pipes to both the kitchen and hot-water seem secured. Is this water hammer? If so, should I get a water hammer arrestor? And finally, does this belong near the kitchen mixer tap or near the hot water cylinder?
If it is only the mixer tap that causes the issue then fit it close to that.
It is not surprising as those short action lever taps shut off the flow quicker than the taps requiring a turn or two to stop the flow.
If two taps cause this then either you need two arrestors or one where their supply pipes combine. The only issue with this is that any length of pipe between the tap and the arrestor is subject to the pressure pulse that causes water hammer and, if it is weak, it could fail.
Had a situation where a large valve (6" pipe valve) could cause water hammer if it was shut too rapidly (supply to a water turbine) but the surge protection could not be close to that valve - it had to be 60 yards before the valve... So that pipe had to be stronger just in case. The surge protection was a vertical pipe of 32 feet, which would provide a big shower if the valve was shut too rapidly.