I don't have any audio equipment that can detect the buzzing well enough but it can be heard. I would say that the buzzing sound equivelant is your usual case fans humming at idle.
Take the GPU apart and put it back together. Use isopropyl alcohol and compressed air to remove any dust. When you reaffix the cooler, try to identify any points of mechanical weakness where the vibration is originating from. You might be able to apply a mild epoxy, and reduce the whine.