Could be a pressure reducing valve at the main water service.
Could be a worn washer inside the faucet.
Does it happen at a particular faucet or all of them?
If you have the old style ballcocks in you toilets, they can vibrate at the right frequency to send a loud humming noise through out the plumbing system.
You can verify this by touching the float. When the squealing is heard touch the float. If it's vibrating the noise will stop the moment you you touch it.