48kHz and the broken Frequencies
Since we can safely say that any frequency up to 4096 kHz works “fine”, let’s take a look at the frequencies above them. For example, how about we look at integer divisions of 48 kHz and variations of them, such as 19.2 kHz, 16 kHz, 12 kHz, 9.6 kHz, 8 kHz, 6 kHz and 4.8 kHz.
At 19.2 kHz and 16 kHz, we have by far the worst artifacts. It’s not even possible to call these waves anymore, they are just random noise now. Not much of the original wave is left, but we can still guess that it used to be a wave of some type. In the second sample which is slightly offset by time, we can see even worse effects for both frequencies.
Continuing on with 12kHz and 9.6kHz, we can see similar results depending on just how the time offset is adjusted. However good filtering algorithms might be able to still make out that these used to be waves – the velocity of the waveform could be used to recreate a proper wave for the frequency that we are trying to reproduce.
With 8kHz and all frequencies below that, we’ve approached the area where the artifacts become so small that we can filter them out at minimal loss. Knowing this we can infer that all smaller frequencies that this will perform fine, given good filtering.
So the question then is, what sample rate is enough to fix the majority of artifacts?