First, we have to understand how sampling works. For that, we need the Nyquist rate. This is the theoretical minimum sampling rate at which a signal can be sampled and still be reconstructed without any distortion.
Conversely, a system can capture and recreate frequencies up to half the audio sample rate, a limit called the Nyquist frequency.
44.1 kHz, which means every second of audio contains 44100 samples. This has a reason. Humans can hear frequencies between 20Hz and 20kHz. This 20-to-20 rule is still accepted as the standard range for everything we could listen to. The computer should be able to recreate waves with frequencies up to 20 kHz. The sample rate of 44.1kHz technically allows for audio at frequencies up to 22.05kHz to be recorded, this is slightly higher so we can use more moderate filters to eliminate aliasing without much audible effect.
48 kHz, commonly used in audio gives more measurements per second and is theoretically closer to the original audio. This sample rate for audio gives more buffer room. 88.2 kHz, 96 kHz, 176.4 kHz, and 192 kHz, Used by some engineers, are all multiples of 44.1 kHz and 48 kHz
So can you hear the difference?
Since filtering and analog/digital conversion technologies keep improving, it becomes more difficult to hear, but in theory, yes.
The higher the sample rate, the closer it is to the original.
*Image by izotope.com