If your car is producing a high-pitched squeaking noise, the first thing you should check is the serpentine belt, or any other belt in the engine. Once you've checked the belts and ensured they are all in working order, you may need to explore other options to track down the source of the sound.
You may be dealing with a faulty tensioner or idler pulley. A tensioner pulley is used to adjust the belt, and if this part breaks or wears out, the belt can become loose or damaged. An idler pulley is essentially the same as a tensioner pulley, but it also helps to guide the belt coming off of a main pulley to reduce vibrations.
If you replace a worn belt and the new one wears out quickly, this could be because a tensioner pulley is busted and needs to be replaced. Until this issue is fixed, expect to replace the serpentine belt frequently.
If rust, corrosion, dirt or other debris jam up the tensioner, it will not be able to turn freely. When this happens, the tensioner won't be able to keep the proper tension on the belt. When the pivot arm becomes loose or worn, it can cause strange noises, as the belt may become misaligned. The bushing may also wear out, and if it seizes, the belt could snap. When the belt breaks, the car will not run until it is replaced.
A tensioner also has a coil spring that applies the precise force needed to keep the serpentine belt just tight enough while still providing a bit of give to absorb any shock. If this spring is weakened for any reason, it may cause belt slippage when the engine is running, which will result in unpleasant noises while you're driving.
The best rule of thumb is to inspect tensioners when you're checking on the health of the belts, which should be done regularly. If you're experiencing trouble with the belt, chances are the tensioners are connected to the problem. When this part is failing, you may also notice the battery is run down, as the belt could be slipping and unable to turn the alternator fast enough to recharge the car battery.
You may also be able to tell if the tensioner needs to be replaced by observing it while the engine is idling. Excessive movement sometimes referred to as "belt flutter" is a sign that the tensioner, and likely the bushing, is worn and needs to be replaced.