Why does my car make noise when I accelerate? I.

They all do. Engines, exhaust systems, transmissions, tires all make noise that gets louder when you accelerate.

Based on that description I'd start by looking at the electric radiator fan. Normally it will not need to turn on when the car is moving since natural air flow through the radiator is sufficient, however, that is about the only thing that will slow down at a different rate than the engine or car.

There is a tool you might be able to borrow or rent from an auto parts store that borrows them called the "Chassis Ear". It is a set of six microphones, a switch box, and headphones. You clip the microphones to suspect points, then drive around while listening with the headphones. You can move the microphones around to zero in on the source of the noise. Be aware that many mechanics have never seen or even heard of this tool. Suspension and alignment mechanics use it to find rattles, squeaks, and other noises.