Math · Physics / Why a note is a wave
Uncut
A spinning stick’s shadow
Why a note is a wave
Hold a piano key. The note sounds “the same” for a while. So why isn’t the air just a flat push — one steady shove that never changes? Your ear needs change. Constant pressure is silence (tryck · ljud). The repeating up-and-down of pressure is the wave. The triangle is only the measuring stick.
— same rim; here the angle keeps turning in time.
— beach fronts vs pressure ripples in air.
— the ratio names you already met.
Origins
chord tables
Sky angles in, lengths out. The table stored the straight chord between two rim points — not the wave plot. Circle first, for the sky.
~499
Half-chord — jyā, a bowstring — became what we call . Full chord is twice that half. The right triangle is the measuring frame at one freeze of the turn.
Euler & sound
Let the angle keep turning: the height plot repeats. Springs, strings, and air pressure swings share that simplest repeating piece. Not because nature forbids other shapes — because this piece is the clean atom.
Honesty: we start from the circle and a spinning radius. We are not dumping a DSP course or every wave shape.
Spin the stick. Plot its height.
Unit circle — radius 1. The radius is a clock hand. Drop a vertical from the tip to the diameter. That height is of the turn. Beside the circle, plot height against how far you have turned. That plot is the wave (sinusvåg · enhetscirkeln).
θ = 35° · height (sin) ≈ 0.57 · the plot is that height over the turn
Left: freeze one moment — right triangle (radius, horizontal, vertical). Right: keep turning — the height line draws the wave. The triangle did not cause the wave; the circle did.
Snurra radien. Höjden är sin θ. Plotten höjd mot vinkel är vågen — inte en triangel som springer runt.
Freeze one moment — keep turning
Same circle, two jobs. Triangle = snapshot. Wave = the turn written as a graph against time (or angle).
Air carries squeeze, not a drawn sine
Sound is not a floating sine curve in the room. Air carries denser and thinner pressure — a squeeze traveling along, like a slinky compressed along its length (ljudvåg · tryck). At one spot — your eardrum — pressure goes up and down. That up-down can look like the plot you just drew.
= how often the swing repeats — pitch. = how far the swing goes — loudness. = the colour of the sound — which simple pieces are stacked.
A guitar or piano starts with a bright attack: many higher pieces ride along. Those higher pieces fade first. What is left is a simpler leftover wave. Bright attack, then the colour drains — the leftover is quieter and simpler. (klangfärg · övertoner).
“Same note” ≠ flat line. A flat line would be constant pressure — silence. “Same” means the repeating cycle holds steady while you hold the key.
Job: why does a held piano key still need a wave, not a shove that never changes?
Sine is the simplest piece — not the only wave
Sine is the simplest restoring-force mode and a clean building block. It is not the only wave. Square, saw, and triangle shapes exist too (electronics, old game chips, synths). Any repeating shape can be stacked from simple sine pieces — — the clean atoms, not a law that forbids corners (harmoniska · Fourier — later wall).
Next wall, not this page: building odd shapes from many sines. We stop at “simplest repeating piece.”
Bits vs harmonics — two different “how many”
How many amplitude steps we store is not how many sine pieces are in the sound. Sample rate asks how often we measure. Bit depth asks how far we can tell loud from a little less loud — steps of loudness detail. Harmonics ask about the colour of the sound — the sine pieces stacked inside.
At very few steps (1-bit: only two levels, on/off) different instruments collapse toward the same harsh staircase. With finer steps the attack and colour return. Label below: loudness steps, not more harmonics.
1-bit · 2 loudness levels · instruments collapse toward the same on/off look
Grey ghost: a richer attack (colour). Black stairs: the same shape with only N loudness levels. Steps of detail — not extra harmonics.
Bitar = hur fint vi sparar ljudstyrka. Harmoniska = vilka enkla vågor som ligger i klangen. Inte samma fråga.
Try Bitwave — play the same loudness-step lesson with real instruments (Lab + Composer).
Gate — four, all required
Hands-on (change the turn) is 20. Each right gate item is 20.
1. A piano key held down sounds “the same.” Why isn’t that a flat push of air?
2. You spin the radius and plot height vs turn. What is that plot?
3. What does air carry when you hear a note?
4. Recording with more bits means…