What could be causing my air conditioner to make a humming sound?
The usual culprit is resonance. Your pump vibrates at a particular frequency, and while the mountings are usually damped using rubber bushings enough vibration passes to the floor/wall that anything else nearby that resonates at that frequency will vibrate if not fixed securely.

Ducting should be your first check, but also floor boards, drywall panels, or anything really.