Whirring when starting

I have a 98 GMC Safari.
Lately when I go out to start it, I get a whirring for about 30 seconds then it goes away.
I can't hear it from the inside, only when I have the hood up. The reason I was looking was because I just had the belt changed.
Since it doesn't last long, I'd normaly blow it off but I've been paranoid lately since it threw the belt while I was driving down the road and I've worried about it ever since.
Any idea what the sound could be?

Since you just changed the belt ya need to look into why the belt came off. Serpentine belts rarely break. Could be a weak belt tensioner or a loose idler pulley. Check pulley alignment also.

Belts don't get thrown off for no reason-- just replacing the belt is like putting air in a leaky tire---you need to fix why that belt came off- and I'll bet that whirring goes away too.....

Look for a tight component or a bearing that is wearing out/locking up.