Digital audio is underpinned something called the Shannon-Nyquist sampling theorem. This theory from way back in 1949 and relates to all information but is particularly important to the study of audio.
What the theory tells us is that any continuous signal (including sound) can be represented by a series of samples taken at twice the highest frequency contained within it.
It is common to refer to the nyquist frequency (),the highest frequency that can be represented at a given sampling frequency (). They are related by the formula
The range of human hearing is at its very best 20 KHz. Sampling sound signals audible to humans therefore requires a sampling frequency of at least 40KHz.