noise
RedEG6C: Maybe it's an exhaust leak at the exhaust manifold gasket. When you are not getting much pressure coming out, it can leak, then when you speed up it hits its target and funnels down through the exhaust. This sometimes happens when people modify the exhaust with a full catback or a high flow cat, pulls on the header and the gasket gets warped. That's just a suggestion tho, if you asked a mechanic in person he could probably tell u in a second...
superSol: Is it possible the alarm system speaker in your engine bay is loose? I know it sounds dumb but that happened to me... just tightened the screw and those symptoms disappeared.