Why a faucet whistles can have several different causes. Something loose in the water stream can vibrate as the water runs by it causing a whistling noise. The whistling sound can also be caused an unusually high velocity flow of water passing through a restriction. The problem does not even have to be in the faucet itself but instead may be in the pipes or stop valve installed below the faucet feeding the faucet with the sound transmitting up to the faucet. It may help if you know whether the whistling happens only with the hot or, the cold or, both. This can steer you to whether the problem is before or, after the two different water temperatures are mixed.
Problems in the faucet after the water is mixed may include things like debris in the aerator, a bad cartridge on single lever or, handle faucets, side sprayer diverters on kitchen sink faucets, and on tub/shower mixers loose washers on the shower diverter valve or, debris caught in the restrictor for the showerhead. Basically troubleshooting would involve taking things apart and looking for the problem and sometimes flushing the faucet out with things like the aerator or, showerhead removed.
When the sound is on a single temperature in most cases you can eliminate the area where water is mixed. Instead you can concentrate on the side where the problem exists. On faucets where a single lever or, handle is used the problem can still be a bad cartridge, while on faucets with two handles you can go right to the side causing the problem. Shut off the water and remove the stem. Look for things like a loose or, deteriorated washer or, a badly worn stem. If the problem is on the hot side and your water is extremely hot sometimes the extreme heat can soften a faucet washer. Extreme heat can also affect rubber parts down stream from where the water mixes such as the diverter on a kitchen faucet. You may also have to chase single temperature noise problems further down the supply side including the stop valves and their washers and the supply lines and pipes.
Unusually high velocities can also make a whistling noise. This can be caused by high pressure being supplied to your home. The pressure should be less than 80-psi and can often be measured with an inexpensive gauge, which can screw onto a hose bibb. I like to use gauges that have a lazy hand, which will record the highest pressure reached as long at it is attached and water is turned on to the gauge. If the pressure is over 80-psi a pressure-reducing valve should be installed and in most cases thermal expansion tank would be required to be installed on your water heater too. Sometimes pipes may have restrictions, which can cause noise such as a build up of scale or, rust in the case of galvanized pipes.
Finding the source of your whistling noise in the faucet is not always an easy task and in some cases like with the cartridges may require replacement without even knowing for sure that it is the problem. It often comes down to I’ve checked every thing else lets try this.