This whistling noise is correctable as long as you have the tools to make the repair.
About Whistling Sounds
The typical whistling sound occurs in the faucet when the water is on because, when the water is off, there is no water movement to create a sound. In some cases, banging sounds, sometimes called "water hammer," occur after the faucet is turned off, which is a result of the pipes rattling after the water shuts off and is entirely different from whistling sounds. While water hammer is due to built-up back pressure in the pipes, after a direct change in the water flow, whistling sounds come from water rushing past a loose part in the faucet.
Loose Faucet Parts That Whistle
One of the most common causes of whistling in a faucet is a loose seat washer, a small round washer inside the faucet's handle pipe. It is part of the faucet's stem, the valve that closes the faucet and restricts water flow. Since this seat is the surface the stem comes in contact with to stop water flow, it wears out after regular use. As the stem wears out, the washer begins to loosen. When water passes it, the washer flaps around very fast inside the faucet, creating a whistling sound. When this happens, the only way to stop the sound is to replace the faucet stem.
Correcting Whistling Sounds by Removing the Stems
To correct the whistling faucet noise, replace the entire seat in both handles. Start by removing the handle. Loosen the set screw under the cap on top of the handle, and lift the handle off the stem by hand before taking out the stem of the faucet. To do this, unscrew the stem with a special tool called a bath socket wrench, which is designed to remove faucet stems and has a uniquely-shaped socket just for this purpose. Place the wrench on the stem, and turn counterclockwise to remove the stems, which requires some strength as the stems become corroded and blocked with mineral deposits.
Replacing the Stems and Rebuilding the Faucet
Once the stems come out, replace them with new stems. Insert the stems into the pipe, and tighten them with the bath socket wrench. The seats must be very tight to create a watertight seal. After installing the stems, replace the handles and tighten the set screws. Always install the right seats for your make and model faucet. If you install stems made for another brand or model faucet, they may not fit properly and will start whistling again. Ask the clerk at a hardware store or plumber's supply outlet for help finding the right faucet stems for your brand and model.