I put the cover back on my case and I could still hear it. So I took the drive out of the case and hooked it up to an old AT power supply to see what it sounded like without the case. It was about the same so the case must not have been blocking much noise. One thing I disovered was that the drive also makes a quiet shhh noise like a fan but of course that doesn't bother me. The whine however is very high-pitched and seems to cut through everything. It's not extremely loud, although I could hear it from at least 6 feet away when not in the case, but it's such a high-pitched noise that it makes it extra annoying. Have you ever turned on a TV and heard a high-pitched noise come from it? Well it's kinda like that.
Also, I got a chance to hear the startup noise. If I'd heard it like that to begin with without all the other stuff in my computer distorting it I never would have worried about it since it's obviously just normal spin up noise.