You will hear it because of the square wave you're feeding it, the mechanical harmoinics in the speaker itself with all the ringing that's going to be produced at that power level will garuntee you hear something. Keep in mind when I said ringing I meant it will go above and bellow where you think a straight stop should be and it will ring back and forth for a short period of time (at a higher frequency) each time it does due to the elasticity, mass, inertia, and velocity of the speaker cone itself.
If what you expect is the physical medium to move from a low position to a high one and back and forth without any other frequencies it will not occur so you need to flesh you what your physical demonstration entails.
If you could feed the same speaker a perfect sine wave of the same frequency it will move up and down gradually and gracefully from one extreme to the other at the same frequency. If you wanted it to go from low to high quickly but without the ringing it gets much more complicated as you have to shape the waveform the speaker gets to avoid the ringing effects. If the mass you're trying to move with the voice coil is anything other than the weight of a needle you'll get more harmonic effects.