Plumbing is persnickety thing. The key to all this is vibration. Since the water is traveling through the pipes as it flows through the pipes, its creating small vortexes (hydrolics) inside the pipe. Depending on the speed these cause the pipes to begin vibrating in frequency to the harmonics created in the pipes. At times they will amplify the sound, just like a tuba. Since the principal is the same. In addition as the water passes through the faucet itself, it can pass over rubber gaskets (depending on faucet type) and set up a fluttering of the gasket, again a vibration is set up and the harmonics cause noise.
If the water travels through the pipes at a greater speed than 10 feet per second, then the pipes will begin groaning. State codes have set regulations on codes to prevent this, but if your pressure is too high and/or your faucet allows too much water to pass through it, these speeds can be exceeded and the sound will begin. Sometimes a pressure reducing valve at the meter lowered to 65 psi can prevent this noise. Have someone check to see that the pressure in the home does not exceed 80 psi.