Originally Posted by Strange Mud
did it start right after new pads? if so some lube on the back of them
someone outside the car with a length of hose as a stethoscope
My money's on this. I sometimes get almost the exact same sound with the Hawk HPS pads I put on my car, usually when the pads are cold. People say the Hawk pads are a bit noisier than stock, and they ain't wrong--this despite greasing the heck out of the backs of the pads, caliper slides, etc., during installation.
OP, regreasing as Mud suggests should help. Slather as much on there as you reasonably can without getting anything on the pad or rotor surfaces themselves.