I've got a couple of taps that for want of a better word "hammer" when
opened a particular amount. In one case - a mixer tap - this causes
the whole tap to vibrate alarmingly and can be heard throughout the
house.

Another one when opened a small amount makes a loud clear tone which
seems to resonate through all the pipes in the house.

I'm curious - is this a fault of the taps, or is it something more
complex?

Some of them at least I'm intending to replace soon anyway.