If your water pump reminds you of a jackhammer on a New York City street, you are not alone. A noisy water pump is one of the most common complaints of RV owners.
Several things can be done to quiet it. The first step is to find the pump. Water pumps are usually tucked away in a cabinet at floor level somewhere; the noise should lead you to it.
Once the water pump has been located, check that the screws holding the pump to the floor are tight. Most water pumps are mounted on a small platform or on rubber mounts and are secured to the floor with three or four screws. The platform or mounts are supposed to keep the pump from vibrating against the floor. Check the mounts to make sure that they are not cracked, worn or missing. The pump itself cannot be insulated because the electric motor needs air circulation to keep it cool. Covering the pump may cause the motor to overheat and fail.
Next, trace the cold water line from the pump to the faucets. If it passes through a cabinet wall or is routed along a cabinet wall, the vibration of the water line may be turning the cabinets into a sounding board and amplifying the vibration and noise just like a musical instrument. Get some lengths of foam pipe insulation the correct size to fit the pipe and put it around the pipes in those places that touch or pass through the side of a cabinet. Water pipes that touch the drain pipe under a sink or shower can also create quite a racket, so put insulation in those places, too. Wrap a piece of duct tape around both ends of each piece of insulation to keep it in place.
It may take some contortions on your part to get the insulation around the water lines since they are often routed behind drawers and at the back of cabinets. Once it is in place, the foam insulation should absorb much of the vibration of the water lines and keep the cabinets from singing.