Even if the wave isn't played with a wavelength of an integer number of samples, a good DAC will produce a pure sine wave as an output (as long as the sine is e

Even if the wave isn't played with a wavelength of an integer number of samples, a good DAC will produce a pure sine wave as an output (as long as the sine is exact, and the wavelength of the wave is 2 or more output samples). If not you get aliasing (or the wave playing at the wrong frequency). This generalizes to non-sine waves, as long as you advance by the same number of waveform samples on each output sample, and the wavelength of the highest harmonic is 2 or more output samples. In practice it's common to have non-exact sine/etc. waves, or not advance by an integer number of waveform samples on each output sample (generating output samples using various interpolation methods), both of which introduce high harmonics which get aliased to the wrong output frequency. For more information on discrete-to-continuous frequencies and reconstruction, you can watch Xiph's "Digital Show & Tell" (https://xiph.org/video/vid2.shtml https://xiph.org/video/vid2.shtml).