It'd be nice to know what kind of car. Well, I figure it's an Accord, but what year & what engine?

I'd guess drive belts (alternator, AC, PS) are too loose. Or maybe just too old & slippery.

But if you got a V-6 they'd be on the wrong side of the car...

Could be brake wear 'indicators', too. Is it different if you drag your brakes when you start up? Look at your brake pads. Are they worn down?

Can you make the noise without moving the car?