Transformer hum is mainly mechanical, usually involving loose core laminations in typical transformers, but can also be loose mounting or "sounding board" affect on chassis, covers or other susceptible components. It occurs because the reversing 60 Hz magnetic field tends to move (vibrate) the ferrous transformer parts and this is coupled mechanically to the mounting. This can be a quality or age issue with the transformer itself. Generally, damping will probably be the primary suggestion you get. Mechanically isolating the transformer, adding material to vibration prone areas, or just isolating the unit from it's supporting structure (shelf). There will probably be many specific suggestions forthcoming.
