When I turn off the kitchen sink faucet, the copper tube behind the refrigerator (that goes to the ice maker) rattles. I pulled the refrigerator away from the wall a couple days ago to clean behind it, and wonder if I could have loosened something. I think I heard some pipe rattling in the kitchen several weeks ago, but the noise came from another area -- the rattling noise happened when I turned off the kitchen sink faucet, but the rattling sound seemed to come from underneath the kitchen (there's a crawlspace there).

My house was built in the mid 1960s -- could there be one of those air pipe gizzmos that has lost its air, so I need to drain the house? And could I have done something to the ice maker copper feed tube when I moved the refrigerator?

Sounds like you are getting a little water hammer. This noise could be the tubing bumping againist a cabinet, I'd secure it with a screwed in clamp. If the noise goes away then you are good to go, if not let us know and we can help install a water hammer arrestor

Your air chambers sound like they're loaded up and must be recharged.
"Water hammer" happens when you abruptly shut off the water. You have at least 40 pounds of pressure pushing the water flow. The weight of the water hitting a 90 degree bend causes the sound that you hear. We put in air chambers to cushion the hammer much like the shocks on your car.
Back in the 60's we were required to to put air chambers on all bath lavatories and kitchen sinks. Over time water and condensate built up in them and they must be recharged. First turn off the house at the main house shut off valve. Then open hot and cold faucets at the farthest bathroom to prevent air lock.(This is important.) You will find under each fixture little brass or chrome valves. These are called angle stops. With a small pail held under the angle stop to catch the run off look under the handle of the stop and you will see a nut with the stem running through it. This is called the bonnet packing nut. Put your wrench on it and back it off counterclockwise. Now open the stop and remove the stem and washer assembly, The stop will began to drain. When it has quit draining reassemble the stop and move on to the next one. Do this on each one of your angle stops. There will be six of them in a two bath home. When you are done, close off the faucets you have opened, turn on the water to the house, and give yourself a pat on the back.
You have just recharged your air chambers and saved yourself a hefty service call bill. Hope this helps you out and thank you for rating my reply. TOM

Howdy,
Does the rattle happen when the kitchen sink is at a very low flow? How old is the Faucet on the kichen sink?