When does 48 kHz run into problems?
The most common case is the conversion from Digital to Analog – without it we would not be able to hear any audio at all. Let’s take a look at a few common frequencies: 32 Hz, 64 Hz, 128 Hz, 256 Hz, 512 Hz, 1024 Hz, 2048 Hz, 4096 Hz, 8192 Hz, and finally 16384 Hz.
Looking at the generated graphs, we can immediately tell that anything equal to or below 2048 Hz will be perfectly fine on 48kHz. We can also tell that somewhere between 2048 and 4096 Hz we will start seeing slight artifacts, and that everything above that unknown value will have ever stronger artifacts – In fact we can see the strong artifacts appear on 8192 Hz already.
And at 16384 Hz we might as well just throw in the towel as there is basically no way to create the original wave with current hardware. Even the most accurate DAC will struggle to recreate the wave properly, and overshoot and undershoot constantly, corrupting the wave past recovery. While it is possible to work around the issue, it won’t be gone.
Knowing this we can tell that for the majority of audible frequencies, we’ll be safe with 48kHz. But so far we’ve only looked at 2^n frequencies – what about other frequencies that end up in a pretty bad shape at this sample rate?