How could a rotating field, produced by the armature in the alternator, create anything but a sine wave? Where could the noise come from?
The frequency is set by the armature (engine) speed, the voltage mainly by the field strength/number of turns on the stator and partially by speed.
Normally on small alternators, the armature is permanently magnetized (or charged), but may have slip rings that drive windings on the rotor and are controlled by a regulator to control the voltage output, but this I would imagine is on larger, more expensive gensets. The smaller portable ones don't have this because of the expense involved. (I think).