Google "Nyquist" sometime. Essentially the jist is you can *flawlessly* reproduce any frequency, by sampling at double the rate.
So if you want a flawless 22khz signal (which you cannot hear), you sample at 44khz. Hence why most music is sampled at 44.khz.
It has absolutely zip to do with the smoothness of the output waveform. You will get a flawless sine with 2 points per cycle.