For a while there had been an annoying buzz emanating from my Mac Pro. I knew it had something to do with a new hard drive I installed, and for a while I thought the drive might be defective, like an earlier one I had that was extremely loud before I returned it.
In this case, it turns out that I had not fully tightened one of the screws on the metal sled that you mount the drive on before sliding it into the case.
The way I found out was that I pulled the drive out of the computer and lightly rapped it with my finger; I could hear something slightly loose and thought it might be the bracket. After I tightened all the screws and slid the drive back into the case, the noise level was back down to normal.