I'm a bit scared to admit this, but here goes…
We have a bunch of Mac Pro's in office. One of them (in a rather quiet room no less) started making a persistent high frequency continual buzz. It was definitely a moving components, because shutting the computer down would stop the sound. Tracing the sound eventually led me to the video card. Despite how low it was spinning, the video card fan was spinning nevertheless. When I would press my finger onto the middle of the fan (forcing it to stop spinning), the sound went away.
At that time the computer was highly highly mission critical, so downtime more than a few minutes was not a good idea. The Apple Store had none of our video cards in stock, and they were unwilling to take my word on the diagnosis and order it.
So, I engineered a 0.01¢ fix. I took a piece of scotch tape, and stretched it across both sides of the fan (the fan is raised with a plastic housing), and smoothed down the middle on the fan's plastic. The fan stopped spinning, and the sound disappeared. The office was quiet again.
Note that this is probably a TERRIBLE IDEA, because it restricts air flow across the video card which is a very hot device anymore. I honestly don't suggest this fix.
But, what I am saying is that you should check out your video card fans, and you can temporarily stop it to see if it resolves the audible issue.
And really, you can try this with every fan, not just the video card fan. Do be careful, however. Despite being plastic, some of these fan blades can hurt.