Sampling Theorem

Nyquist–Shannon: a band-limited signal with maximum frequency $f_{max}$ can be perfectly reconstructed if

$f_s > 2 f_{max}$

$f_s/2$ is the Nyquist frequency. Frequencies above it alias — they fold back and appear as lower frequencies that can't be removed afterwards. Sampling a 900 Hz tone at 1 kHz produces a false 100 Hz tone.

Practical systems put an analog anti-aliasing low-pass filter before the ADC and sample comfortably above the minimum (CD audio: 44.1 kHz for 20 kHz audio).