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My understanding is that most 3-speed floor fans are wired with two sets of windings, one for each target power. I've got a whole-house fan on a heavy-duty dimmer, At very low power settings it hums loudly due to the spikes in the supplied power:
(look up google images on "lamp dimmer ac waveform")
A lamp dimmer usually uses the zero-crossings in AC power as trigger points for a triac switch. The large deviation from sine wave magnifies the hum, but efficiency is still fairly good. There are dedicated fan control switches, but I have not seen a voltage trace to see if that's what the do that is special.
The power usage of your ceiling fan will be on a placard somewhere, but is probably around 60 Watts.
Mark
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