HVAC duct work radiates 60Hz
A stray wire touching the metal frame of the furnace, old wire with insulation falling off touching the ductwork, wire run around a duct and the duct is cutting into the wire, a "leaking" electric motor in the furnace, etc. Any of these could cause the duct work to become energized.
Or a water pipe system to become energized.
Or anything metal running through a house or a building.
For that reason, it is a good idea to bond metal electrically conductive systems like plumbing, natural gas pipes, ductwork, etc. to ground.
This could be a very dangerous situation. If you are not familiar with troubleshooting these sorts of electrical problems, I suggest you call an electrician. I suppose the electrician would run a long wire to ground, then measure with a multimeter from that wire (ground) to the ductwork to see if there was a voltage on it.
You could confirm which circuit it is by turning off one breaker at a time. See which stops the noise in your hearing aid.