the noise begins as soon as the car rolls, and is unrelated to revs as it is unchanged when revving stationary.
So does the car make the noise when the engine is running, but the car is not moving? And then, once you get moving, the noise increases in frequency as speed increases?
If it was only happening when you were moving, I'd say you have something in a tire or something jammed in a brake. If it's the brake, put the car in reverse and back up a bit. This should clear whatever it is.
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