The sound may be produced by some form of a permanent feedback loop to allow a movable lens element to “float” in the air, but does any one know what is, precisely, the origin of the sound? And why it is permanent on Fuji lenses with OIS?
Without power, the OIS element in Fuji lenses (and some others) is free floating. The OIS element isn’t “parked” and locked when the power is removed (unlike, say, read/write heads for spinning hard drives). Thus, the OIS element has to be held “rigidly” in its optically neutral position (non-stabilizing control) at all times when the camera is powered.
As with any system with active feedback control systems, the controller is still working, even if it was commanded to just stay at a commanded point. By analogy, a Harrier VTOL jet that is asked to just hover 100 ft. above the ground is still working its control systems. The controller is always trying to compensate for error inputs, such as gusts of wind that might move the jet laterally or change its altitude.
Functionally, the only difference between enabling and disabling OIS in these types of lenses is whether or not the feedback control system is trying to filter out (i.e., compensate for) motion frequencies around 20 Hz and lower. ST Microelectronics has an interesting white paper discussing OIS controller design and implementation, that covers this in more depth.
This controller has to be almost immediately responsive to movement, so the feedback controller is operating at much higher frequencies than just the 20 Hz (and below) that needs to be filtered. It’s this controlling frequency moving the OIS element that is the source of the noise. In essence, the OIS element is acting like a speaker cone — a thin, more-or-less planar surface moving to some degree back and forth (although it’s mostly just laterally) pushes air around. Because it’s controlled by electromagnet motors, the moving OIS element is also pushing back on the lens body itself. Some of the motion is in the audible range of human hearing, which is the buzzing sound you hear.