I was able to track down the cause of the problem. Pull out the water tank and look into the machine. You will see two silicon gaskets for sealing the air lines between the machine and the water tank. One or both of these is the source of the noise.
I ran my finger around the inside edges of each gasket to make sure it was seated in the plastic and still round. I put the water tank back in the machine and the noise was gone.
Somehow an air leak gets started there and the silicon starts vibrating and squealing, the sound changes depending on inhale or exhale.