A dishwasher is better diagnosed by diving into it than from the comfort of a keyboard, noting if it happens at a certain cycle or all the time, and finding the origin of the noise.
Obtain its service instructions. It will help with your irritation.
Observe the point in the cycle that the buzzing occurs, e.g. if filling or draining, AC solenoids can make an annoying buzz when uneven seating of the armature occurs.
M.