In digital audio every sound is a long sequence of numbers between −1 and +1 — one per sample, 44 100 of them per second at CD rate. Each number is the amplitude at that moment: the instantaneous pressure of the sound wave, or the displacement of the speaker cone. 1.0 is the loudest the system can encode; 0 is silence. Doubling amplitude doubles the cone displacement — but does NOT double the perceived loudness, because loudness is logarithmic.

Used in: the L/R channel readouts, the −1 to +1 axis of the oscilloscope.

That ±1.0 limit is not a physical law — it’s the floating-point convention that says "this is the loudest value the format can carry." Anything beyond ±1.0 gets CLIPPED: the tops and bottoms of the waveform are shaved off flat, replacing smooth sine peaks with harsh corners. Those corners are harmonic distortion that no normalisation, no EQ, and no AI restoration can ever undo. The dBFS scale measures relative to this 1.0 reference: 0 dBFS = exactly full scale, −6 dBFS = half amplitude, −∞ dBFS = silence. Engineers keep audio comfortably below 0 dBFS — typically with 3–6 dB of headroom — so transient peaks have room to breathe without slamming the ceiling.

Used in: every dBFS readout. 0 dBFS is the line you don’t cross; the −3 dB fix sits at 70.8 % of full scale.

A sine wave is the simplest possible oscillation — a single frequency, perfectly smooth. Every complex sound is a sum of sines at different frequencies (Fourier). The functions sin(θ) and cos(θ) draw the same shape, just offset by a quarter cycle. θ is measured in radians: one full cycle = 2π, half = π, quarter = π/2, eighth = π/4. So "θ = π/4" means "45° around the circle" — the exact midpoint of a quarter rotation. That midpoint is where cos(θ) = sin(θ) = √2/2 ≈ 0.707 — the equal-power center pan.

Used in: the equal-power pan curve from section 02. Slider t = 0 → θ = 0; t = 1 → θ = π/4.

Acoustic power is the energy a sound delivers per unit time — watts of sound, essentially. Power is proportional to amplitude squared (P ∝ A²), so doubling amplitude quadruples power. Two speakers playing the same signal deliver twice the power of one speaker — and doubling power equals +3 dB by definition. That single fact is the whole reason the dual-mono attenuation has to be −3 dB.

Used in: the "power = amplitude²" math in section 03, the +3 dB rule.

Loudness is the subjective experience of how loud a sound seems. It is NOT the same as amplitude or power. The ear is most sensitive at 1–4 kHz (where speech lives) and far less sensitive at sub-bass and ultrasonic frequencies. It also integrates over a ~400 ms window — a single-sample spike is inaudible. Engineering standards like LUFS, dB(A), and sone are different approximations to perceived loudness, never the exact thing.

Used in: everywhere the page says "perceived" — distinct from raw amplitude or RMS energy.

A decibel is a ratio expressed on a logarithmic scale. For power: dB = 10·log₁₀(P/Pref). For amplitude: dB = 20·log₁₀(A/Aref). The scale is logarithmic because hearing is logarithmic — every +10 dB sounds roughly twice as loud, regardless of where you start. 0 dB is not silence; it means "exactly the reference." +3 dB is doubling power. +6 dB is doubling amplitude. −∞ dB is true silence.

Used in: every loudness readout. dBFS = dB relative to digital full scale (1.0).

Two sound sources arriving at the same point can combine in two extreme ways. Identical, in-phase signals add as AMPLITUDES — coherent → 2× → +6 dB. Signals with random phase relationships at the listener add as POWERS — incoherent → 2× power → +3 dB. Real stereo playback lives between the two, but the brain integrating two ears with path differences and room reflections sits closer to incoherent. That’s why the practical, conservative rule is +3 dB.

Used in: the "3 + att" formula in section 03. Pick +3 dB and you’re safe; +6 dB is the worst case.