Three way bulbs actually have two incandescent filaments in them. As you rotate the switch on the three way socket through its four positions 120 volts of electricity is sent through the low watt filament, the high watt filament and then through both filaments. Of course that fourth position is back to both filaments unpowered. Yes, if one of the filaments burns out you only enjoy an odd sequence of operation when the surviving filament is energized. If you don't have any three way replacement bulbs you can use a regular screw base incandescent or CFL in the three way socket as a substitute. Everything gets the full wave form at 120 volts 60 Hz whenever it's activated.
Note that in the US household outlets and overhead lighting fixtures might supply voltages anywhere in the 115 to 120 volt range. Central air conditioners/heat pumps, electric ranges, electric water heaters, electric clothes driers and larger window air conditioners are usually supplied with twice the voltage supplied in the ordinary outlets.