Digital audio must sample at least twice the highest frequency to capture it

Evidence

What factors determine how often and with what accuracy we need to sample the sound? It is quite clear that sampling the SPL 100 times a second is a nonstarter—for example, a 100 Hz sinusoidal pure tone has an SPL of 0 one hundred times every second. Just to be sure that the 100 Hz tone is there, we would have to sample the sound twice as often—here at least 200 times per second—to make sure we captured it. Then, you would capture both the peaks and valleys of the sinusoid too. This is the content of the Nyquist sampling theorem; you can see why it is true from the preceding discussion. But we have to do much better than 100 Hz; if we want to faithfully reproduce a 20,000 Hz sinusoid, or least represent its presence, we had better sample at twice that rate, or 40,000 Hz. Indeed, most digital sound recording samples at 44,100 Hz. But since this is right at the theoretical threshold where one might start to hear effects, some sound is sampled at 96,000 Hz, and sound that is to be slowed down later (now we’re talking about research purposes) is sampled even more often. — Eric J. Heller, Why You Hear What You Hear- An…, 487

Categorization

• DEFINE: Explains the Nyquist sampling theorem with a concrete 100 Hz example.
• XREF: connects to: Digital audio capture is governed by sampling rate and bit depth — Almo Farina, Soundscape Ecology: Principles,…, 1948