Both of my outside faucets make anywhere from a chatter to a high pitched squeal. The amount of pressure determines how noisy they are. Why? How can I fix them?

You have loose washers or loose stem inside the faucets. Pressure vibrates with loose washer. Replace washers or tighten up the stem. But the best fix is to go to Home Depot, purchase 2 new faucets, install them, and you are free of troubles for the next 5 years.

Milo is correct it could be the washers and they are very easy to replace them, if it come to the faucets they are not too expencive.

Can you tell us what kind of faucets do you have, hope fully they are not the sweat type, if you will post a picture will be nice,Thanks.

Regards,
John