Generally tranny's use straight-cut gears for the reverse. Straight-cut gears are cheaper to make, but are noisy, esp. at higher rpms. This noise is exacerbated when the gears and fluid are cold.
The old-school GM big block musclecars sometimes had the Muncie "rock crusher" 4spd that was famous for making that noise... in all four forward gears! Straight-cut gears are stronger but noisy. Rent, borrow, or steal an old movie called "Two-Lane Blacktop." The 55 chevy has a muncie that whines in all the gears.
I digress. Probably nothing wrong with your machine. Probably your trans instead of the cars rear.
Hope this helps