Perhaps a silly question, but does turning it off and back on again also resolve the problem?
I can occasionally hear such noises from monitors, and have always thought it was some kind of interaction with the phase of the AC power and some kind of internal physics of the monitor. Generally, turning it off and back on again fixes it for me.
I realize now I have never thought to keep track of a sample which triggers the phenomenon, and I can't really find time to probe for one right now.
I'm not entirely certain, but as I recall it switching it off and back on again is not effective against this issue. I've tried, no doubt, but the only thing noted which seems to have an effect (while the screen is active) is removing the text from display.
When we were teenagers, my friend used to call it "waving a dead chicken". He coined this term to describe the way he would resurrect dead inkjet printers that even I gave up on - by disassembling and reassembling them until they started to work again, while being perfectly open that he has no idea how it could fix the problem, just that in practice it often did.
While this was just a funny term and pretty absurd approach for fixing things (even though it worked!), I took away from it an important realization: the scope of possible causes of a weird, randomly-occuring problem is much larger than I'd normally assume. Over the years, I learned to identify some "outside context" things for computers - ESD, thermals, UV exposure, RF interference, voltage spikes in power lines, devices being almost but not quite connected. Because of that, when in a bind, "waving a dead chicken" may just be called for - in forms of e.g. percussive maintenance (hitting the thing with a wrench), moving things around, switching cables, disassembling, etc.
I don't honestly think turning it off and back on would do anything, either. I also don't have one of those chairs, nor do I want to buy one and use it to test the theory. But, turning it off and back on again is a simple and easy thing to do that should be reasonably safe for the equipment. There is, after all, a reason why power cycling equipment is often a first step to diagnosing and/or fixing weird problems. :)
I can occasionally hear such noises from monitors, and have always thought it was some kind of interaction with the phase of the AC power and some kind of internal physics of the monitor. Generally, turning it off and back on again fixes it for me.