A small water supply leakinside of a building cavity can produce a noise that is hard to track down. Supply pipe leaks may be continuous (and thus are eventually discovered by water stains or mold) or intermittent, such as a leak around a tub or shower control that drips into the wall ...
Also, look, first, for piping that needs to be secured - the sudden surge of pressure when the pump turns on may be causing that movement that can lead to a leak. On 2023-01-09 by Scott I have a submersible well at my home. It is the original well pump, installed 1996. I have ...