Faucets should be seen, and not heard, especially when they scream and whistle odd tunes whenever turned on or off. There are several causes of this assault on your ears. One them is restricted water flow, typically the result of pipes that are too small, or the formation of scale often found with older properties. If either of these is the case, you have no choice. You'll need to replace the pipes. And that translates to a major expenditure of time and money.
Fortunately, the much more common and far less costly reason for noisy pipes lies in a little component known as a washer. If a faucet washer is either the wrong size or insecurely attached to the stem, the result often is unwanted sound effects. The solution is simple - either tighten the washer or replace the unit with a new one. (Naturally, you'll want to turn off your water supply before you leap into operation washer repair.) If the noise persists after you replace or tighten the washer, have a look at the washer seat. Sometimes residue can cause this part to become partially closed, restricting water flow enough to unleash some harsh whistling.
If your faucet squeals when the handle turns, the stem's metal threads are pressing against the faucet threads. Simply remove the stem, and lubricate each set of threads with a coating of petroleum jelly. If the sound effects continue, you're likely dealing with worn threads. First, install a new stem to see if that does the trick. If it doesn't, worn faucet threads are to blame. In that case, your sole option is installing a new faucet, which fortunately is a fairly simple job.