Dick, your floors have gone through 5, or so, major expansion and contraction cycles. Wood is always moving but so slowly that we can't see it.
With any wood floor, you eventually get to the point that the nails that hold the flooring to the joists vibrate as the wood moves up and down on them. In this case, it's the nails that are holding the plywood down to the joists that are squeeking. If you can easily move the carpet, I would run a few drywall screws through the plywood into the joists.
You probably will not be able to remove and replace the carpet easily and you will not be able to find the joists easily unless you do. Therefore, you can use either the metal brackets that they make for this or a piece of 2x stock cut at a 45 degree angle to make a triangular piece to fit next to the plywood and the joist from under the floor. Run drywall screws through the bracket and into the plywood at a sharp angle so it doesn't go into the carpet. Then have a helper stand on the squeeky spot and run screws into the joist.
If you can't picture what I'm trying to say, let me know and I'll try again. Getting to the problem may be a lot tougher that the "fix".