> I disagree with this statement. something can be reproduced, but not neccessarily _perfectly_
This may be confusing two ways to look at it: as mathematical issue, or as engineering problem. Mathematically the discrete representation and the analog waveform are interchangeable: you can get from one to the other. The quality of the conversion between the two can be made as arbitrarily high as you desire -- typically design targets are set beyond assumed limits of human perception.
>also, any time you have more than one frequency involved, they are going to mix in your sensor, and so you are going to have energy above this frequency.
Intermodulation distortion can generate extra tones, and depending on how strong the effect is, they may even matter. Such nonlinearities do not need more than one frequency, though.
This is normally an undesirable artifact, and our ADC/DACs have evolved to a point where they are essentially perfect with respect to this problem. In any case, from viewpoint of a digital system, artifacts that occurred in the analog realm are part of the signal, and are processed perfectly once captured.
> I am in no way saying that people hear in the ultrasonic directly, However I am saying that some people listening to a 15KHz sine wave vs a 15KHz square wave will be able to hear a difference.
The amusing thing is that a 44.1 kHz representation of a 15 kHz square wave will look identical to a 15 kHz sin wave, because none of the pulse's harmonics are within the passband of the system. Do you happen to have a reference where a system such as this was tested with test subjects so that it would be possible to understand how such a test was conducted?