It is the rule that says how often a computer must take snapshots of a sound to capture it perfectly.
Sample at 2x the top frequency and the wave is captured (top); sample too slowly and a 30 kHz tone folds into a fake 18 kHz whine (bottom).
What it is
The rule that says you must sample a sound at least twice its highest frequency to capture it perfectly.
Key facts
Nyquist rule: sample rate must be at least 2x the highest frequency you want to keep (fs greater than or equal to 2 x fmax).
Nyquist frequency = half the sample rate; it is the highest frequency that rate can record (fs / 2).
Human hearing tops out around 20,000 Hz (20 kHz), so you need at least 40,000 samples/sec.
CD audio = 44,100 Hz (44.1 kHz); the extra ~4.1 kHz is headroom for the anti-alias filter.
Pro/video audio = 48,000 Hz (48 kHz); the broadcast and film standard.
High-res rates: 88.2 kHz, 96 kHz, 176.4 kHz, 192 kHz (multiples of the two base rates).
Symbols in words: fs = sample rate (samples per second), fmax = highest frequency captured, fN = Nyquist frequency = fs / 2.
Aliasing = breaking the rule; a too-high frequency folds back and shows up as a fake LOWER tone (the wagon-wheel effect).
Fold-back formula: a frequency f above Nyquist appears at fs - f (e.g. 30 kHz at 48 kHz sampling folds to 18 kHz, an audible whine).
Anti-aliasing filter = a low-pass filter BEFORE the converter that kills everything above Nyquist so nothing can fold.
How it works
Decide the highest frequency you need to keep (for full-range audio, ~20 kHz).
Double it to get the minimum sample rate (20 kHz x 2 = 40 kHz).
Add headroom for the filter, landing on a real standard (44.1 or 48 kHz).
Run the incoming signal through an anti-alias low-pass filter first.
The converter takes that many snapshots per second, each frozen as a number.
Playback joins the dots back into a smooth wave; nothing above Nyquist survives.
Real examples
CD ripped to your laptop: 44,100 samples every second per channel.
A film shoot's audio recorder set to 48 kHz so it locks to video.
A 25 kHz ultrasonic remote tone recorded at 44.1 kHz folds down to a 19.1 kHz ghost whine.
Telephone audio sampled at only 8 kHz, so it cuts everything above 4 kHz and sounds muffled.
A studio tracking at 96 kHz to give plug-ins headroom before downsampling to 48 kHz.
How it helps in live sound
Set the whole show to 48 kHz so consoles, recorders and video all stay in sync.
Never mix sample rates on one network (Dante/AES67 lock everything to one clock, usually 48 kHz).
Match your multitrack recorder to the console rate or you get clicks and drift.
Higher rates (96 kHz) eat double the storage and DSP for little audible gain at gigs; 48 kHz is plenty.
Trust the desk's built-in anti-alias filters; they are why super-high frequencies never alias into your mix.
If a wireless or RF tone sounds like a faint fixed whistle, suspect aliasing fold-back, not a bad cable.
Everyday analogy
It is like filming a spinning wheel: snap photos fast enough and it looks smooth, but too slow and the wheel appears to spin backwards (a fake, wrong motion) which is exactly aliasing.
Watch out
Myth: 44.1 kHz only captures up to 22 kHz so it must sound worse; truth: humans cap at ~20 kHz, so 44.1 kHz already captures everything you can hear, and going below the 2x rule (not above it) is what loses the top.
Fun fact
The "wagon wheel" effect in old Westerns, where spoked wheels appear to spin backwards, is visual aliasing: the film's 24 frames/sec is sampling the wheel too slowly, the exact same theorem at work in your eyes.
Key takeaways
Sample at least twice the highest frequency, full stop.
Nyquist frequency = sample rate divided by 2.
44.1 kHz and 48 kHz exist because hearing stops near 20 kHz.
Break the rule and high tones alias into fake low tones.
An anti-alias filter before the converter prevents the fold-back.