When I turn on the hot water in my shower there is a loud clunking sound. I'm afraid the vibration may cause a joint to loosen and leak. Any idea as to why this is happening and what I can do to correct it? The house is 57 years old and I think the plumbing is original. Thanks.
Sounds like a classic case of a "water hammer".
If you have access to the feed line anywhere (even in the basement) you should be able to confirm the hammering by placing a hand on the line when someone else turns on/off the faucet. You will feel the line kick at the moment you hear the sound.
One fix is to install a cushion (foam, rubber, etc) around the pipe where it makes contact with the joist or nearby wood, or add additional hangers onto the pipe to prevent the line from moving freely. It's also possible to install a "hammer arrester" which contains a small diaphragm which prevents the water flow from stopping suddenly.