I am playing the GOTY edition through Steam. All my sound drivers are up to date.
When I am in the room just before the vault entrance (at the very beginning of the game) there is a faint beep or chirp or click sound in the background. When I walk into the actual vault entrance chamber it becomes a lot louder, and continues after leaving the vault altogether. It is extremely annoying, and makes the game pretty much unplayable. Has anyone heard of this or have any solutions?

Here's a video I shot with Fraps:
http://www.youtube.com/watch?v=Sfk00c5aqG8

I some times have the same problem, however with me it's the sound of a gatling laser whirring.... so far the only option I've found is to save and reload that usually works...

Yea, I've definitely tried that before. I've even restarted, and played through the beginning twice, but it always happens at the exact same place.

I just discovered that the glitch is tied to the music setting in the game. When I go into the setting menu, while in-game and turn the music portion all the way down, the sound glitch goes away. This doesn't solve my problem though. While I can play it now, I still want to be able to hear the music.