My parents had a York furnace for years that was from the early mid-eighties. It did not have a fan for the exhaust, just the blower for the duct work. It also had a pilot light and not the electronic ignition that the newer furnaces use. The blower motor usually has a shaft that turns a "squirrel cage" type fan. I think the whole fan unit uses rubber bushings to dampen the vibration. A bearing in that part may be going bad. Something similar happened to theirs. It was also the blower for the AC so it ran most of the year.
My neighbor has a 6 year old Gas pack and the exhaust fan fins had rusted and designated causing the unit to over heat back at the start of the season. If you change the speed, just make sure the heat exchanger doesn't get too hot on medium. It may be designed for the full air flow of the High setting.