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<script src="https://learn.mimmsy.com/learn-widget.js"></script>
<learn-widget name="decibels-ruler"></learn-widget> It is CC-BY-4.0: keep the credit line the frame shows.
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Fork
A fork is a copy whose manifest names its parent and the parent's version; lineage is kept forever, and the copy is yours to change. The library is its own repository: clone it, copy decibels-ruler/ to a new name (one DNS label), set forkedFrom to { "name": "decibels-ruler", "version": 3 }, change what you want, run npm run check, and open a pull request. Passing the check is the whole gate. Without a checkout, submit the same files to POST /api/widgets and it is served instantly as an unreviewed draft.
Source
The whole widget is these files; the repository has their history.
widget.json
{
"name": "decibels-ruler",
"title": "dB ruler",
"version": 3,
"claim": "A level in dB is 20·log₁₀ of an amplitude ratio, so doubling the amplitude adds 6.02 dB and multiplying it by 10 adds 20 dB, from any starting level.",
"summary": "Slide the level from −48 to +100 dB and watch the amplitude and power ratios; the ×2 and ×10 buttons advance the marker by the same step every press.",
"topics": [
"audio/decibels",
"math/logarithms"
],
"aliases": [
"dB",
"decibel",
"level",
"amplitude ratio",
"power ratio"
],
"check": [
{
"q": "Doubling the amplitude changes the level by",
"options": [
"+3 dB",
"+6 dB",
"+10 dB",
"+20 dB"
],
"answer": 1,
"why": "20·log₁₀ 2 ≈ 6.02 dB."
},
{
"q": "+20 dB means the amplitude ratio is",
"options": [
"2×",
"10×",
"20×",
"100×"
],
"answer": 1,
"why": "10^(20/20) = 10; the power ratio is 100."
},
{
"q": "Why does the amplitude formula use 20 where the power formula uses 10?",
"options": [
"Power is proportional to amplitude squared, and squaring doubles the logarithm.",
"Amplitude is measured twice per cycle.",
"The choice is a convention, and either factor would work.",
"Hearing is twice as sensitive to amplitude."
],
"answer": 0,
"why": "P ∝ a², so 10 log₁₀(a²) = 20 log₁₀ a."
},
{
"q": "A meter reads exactly 0 dB. What does this indicate about the signal?",
"options": [
"The signal is equal to the reference; the ratio is 1.",
"The signal is silent.",
"The signal is at the threshold of clipping, regardless of the reference.",
"The signal is too small to measure."
],
"answer": 0,
"why": "10 log₁₀ 1 = 0, so zero dB marks the reference itself. Silence would be −∞ dB."
}
],
"height": 440,
"requires": [
"logarithms-ruler"
],
"forkedFrom": null,
"authors": []
}
index.html
<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>dB ruler</title>
<style>
/* Default palette so the widget looks right before the host's theme message
arrives (and when opened standalone). The host overrides these on mount. */
:root {
color-scheme: light dark;
--bg-card: #efe9da;
--border: #d8cfba;
--text: #211d14;
--text-dim: #6e6553;
--accent: #31597f;
--accent2: #b04e1b;
--hot: #a82433;
--ok: #3d6b4f;
--ink-rgb: 33, 29, 20;
--serif: "Iowan Old Style", "Palatino Linotype", Palatino, "Book Antiqua", Georgia, serif;
--mono: ui-monospace, "SF Mono", Menlo, Consolas, monospace;
}
@media (prefers-color-scheme: dark) {
:root {
--bg-card: #1e1b15;
--border: #383225;
--text: #e9e3d3;
--text-dim: #9c917c;
--accent: #8fb8e0;
--accent2: #dd9355;
--hot: #df7a88;
--ok: #82bd97;
--ink-rgb: 233, 227, 211;
}
}
* { box-sizing: border-box; }
html, body { margin: 0; }
body {
background: transparent;
color: var(--text);
font-family: var(--serif);
}
.widget {
background: var(--bg-card);
border: 1px solid var(--border);
border-radius: 4px;
padding: 22px;
}
.control-row.sym.single {
display: grid;
grid-template-columns: 88px 1fr;
gap: 12px 16px;
align-items: center;
margin-bottom: 14px;
}
.control-row label { font-size: 14.5px; color: var(--text-dim); white-space: nowrap; }
.ctl { display: flex; align-items: center; gap: 10px; min-width: 0; }
.ctl input[type="range"] { flex: 1; min-width: 0; }
.ctl .val { flex: none; width: 64px; text-align: right; font-size: 13px; }
input[type="range"] { accent-color: var(--accent); }
@media (max-width: 600px) {
.control-row.sym.single { grid-template-columns: 64px 1fr; }
}
.mono { font-family: var(--mono); }
.chips { display: flex; gap: 8px; flex-wrap: wrap; margin-bottom: 6px; }
.btn, .chip {
font-family: var(--mono);
font-size: 12.5px;
color: var(--text);
background: transparent;
border: 1px solid var(--border);
border-radius: 3px;
padding: 6px 13px;
cursor: pointer;
transition: border-color 0.15s, color 0.15s;
}
.btn:hover, .chip:hover { border-color: var(--accent); color: var(--accent); }
.plot { display: block; width: 100%; height: 220px; margin-top: 8px; }
.readout-row { display: flex; gap: 28px; flex-wrap: wrap; margin: 14px 0 0; }
.readout { text-align: left; }
.readout .big {
display: block;
font-size: 28px;
font-weight: 600;
color: var(--accent);
line-height: 1.1;
min-width: 5ch;
}
.readout.accent .big { color: var(--accent2); }
.readout small { color: var(--text-dim); font-size: 12.5px; }
</style>
</head>
<body>
<div class="widget">
<div class="control-row sym single">
<label for="db-a">amplitude ratio</label>
<span class="ctl wide"><input type="range" id="db-a" min="0" max="1000" value="500"><span class="mono val" id="db-a-label">1.00×</span></span>
</div>
<div class="chips">
<button class="btn" id="db-x2">×2 amplitude</button>
<button class="btn" id="db-h2">÷2 amplitude</button>
<button class="btn" id="db-x10">×10 amplitude</button>
<button class="chip" data-db="0">0 dB</button>
<button class="chip" data-db="-6.0206">−6 dB</button>
<button class="chip" data-db="96.33">16-bit span</button>
</div>
<canvas id="db-canvas" class="plot"></canvas>
<div class="readout-row">
<div class="readout">
<span class="big mono" id="db-amp">1.00×</span>
<small>amplitude ratio · a/a ref</small>
</div>
<div class="readout">
<span class="big mono" id="db-pow">1.00×</span>
<small>power ratio · (a/a ref)²</small>
</div>
<div class="readout accent">
<span class="big mono" id="db-db">+0.0</span>
<small>level · dB</small>
</div>
</div>
</div>
<script src="/w/_sdk/host.js?v=1"></script>
<script src="widget.js?v=1"></script>
</body>
</html>
widget.js
/* dB ruler: a level in dB with its amplitude and power ratios; ×2 amplitude is always +6.02 dB. */
(() => {
'use strict';
const $ = (id) => document.getElementById(id);
const rootStyle = getComputedStyle(document.documentElement);
const tv = (n) => rootStyle.getPropertyValue(n).trim();
const wash = (a) => 'rgba(' + tv('--ink-rgb') + ',' + a + ')';
let ACCENT, ACCENT2, DIM, INK;
function readTheme() {
ACCENT = tv('--accent'); ACCENT2 = tv('--accent2');
DIM = tv('--text-dim'); INK = tv('--text');
}
const DB_MIN = -48;
const DB_MAX = 100;
let db = 0;
const sliderToDb = (v) => DB_MIN + (v / 1000) * (DB_MAX - DB_MIN);
const dbToSlider = (d) => Math.round(((d - DB_MIN) / (DB_MAX - DB_MIN)) * 1000);
function fmtRatio(r) {
if (r >= 10000) return r.toExponential(1) + '×';
if (r >= 100) return r.toFixed(0) + '×';
if (r >= 1) return r.toFixed(2) + '×';
return r.toFixed(3) + '×';
}
function setupCanvas(canvas) {
const dpr = Math.min(window.devicePixelRatio || 1, 2);
const w = canvas.clientWidth;
const h = canvas.clientHeight;
canvas.width = Math.max(1, w * dpr);
canvas.height = Math.max(1, h * dpr);
const ctx = canvas.getContext('2d');
ctx.setTransform(dpr, 0, 0, dpr, 0, 0);
return { ctx, w, h };
}
function renderDb() {
const amp = Math.pow(10, db / 20);
const pow = amp * amp;
$('db-a-label').textContent = fmtRatio(amp);
$('db-amp').textContent = fmtRatio(amp);
$('db-pow').textContent = fmtRatio(pow);
$('db-db').textContent = (db >= 0 ? '+' : '') + db.toFixed(1);
const { ctx, w, h } = setupCanvas($('db-canvas'));
ctx.clearRect(0, 0, w, h);
ctx.font = '11px ui-monospace, Menlo, monospace';
const m = { l: 28, r: 28 };
const rw = w - m.l - m.r;
const X = (d) => m.l + ((d - DB_MIN) / (DB_MAX - DB_MIN)) * rw;
const ry = h * 0.54;
ctx.strokeStyle = wash(0.35);
ctx.lineWidth = 1.4;
ctx.beginPath();
ctx.moveTo(m.l, ry);
ctx.lineTo(w - m.r, ry);
ctx.stroke();
for (let d = DB_MIN; d <= DB_MAX; d += 6) {
const major = d % 24 === 0;
ctx.strokeStyle = wash(major ? 0.4 : 0.18);
ctx.beginPath();
ctx.moveTo(X(d), ry - (major ? 9 : 5));
ctx.lineTo(X(d), ry + (major ? 9 : 5));
ctx.stroke();
if (major) {
ctx.fillStyle = DIM;
ctx.textAlign = 'center';
ctx.fillText((d > 0 ? '+' : '') + d, X(d), ry + 24);
}
}
ctx.fillStyle = DIM;
ctx.textAlign = 'left';
ctx.fillText('each small tick = one amplitude doubling (+6.02 dB)', m.l, 16);
ctx.fillStyle = ACCENT2;
ctx.beginPath();
ctx.arc(X(0), ry, 4, 0, Math.PI * 2);
ctx.fill();
ctx.textAlign = 'center';
ctx.fillText('0 dB = reference', X(0), ry - 16);
ctx.fillStyle = INK;
ctx.beginPath();
ctx.arc(X(db), ry, 5.5, 0, Math.PI * 2);
ctx.fill();
ctx.fillStyle = ACCENT;
ctx.textAlign = 'center';
const lx = Math.min(Math.max(X(db), m.l + 40), w - m.r - 40);
ctx.fillText((db >= 0 ? '+' : '') + db.toFixed(1) + ' dB', lx, ry + 40);
}
function setDb(value) {
db = Math.min(DB_MAX, Math.max(DB_MIN, value));
$('db-a').value = dbToSlider(db);
renderDb();
}
function wire() {
$('db-a').addEventListener('input', () => { db = sliderToDb(+$('db-a').value); renderDb(); });
$('db-x2').addEventListener('click', () => setDb(db + 20 * Math.log10(2)));
$('db-h2').addEventListener('click', () => setDb(db + 20 * Math.log10(0.5)));
$('db-x10').addEventListener('click', () => setDb(db + 20 * Math.log10(10)));
document.querySelectorAll('.chip[data-db]').forEach((chip) => {
chip.addEventListener('click', () => setDb(+chip.dataset.db));
});
let t;
window.addEventListener('resize', () => { clearTimeout(t); t = setTimeout(renderDb, 120); });
}
readTheme();
wire();
$('db-a').value = dbToSlider(db);
renderDb();
LearnWidget.connect().then((host) => {
host.on('theme.changed', () => { readTheme(); renderDb(); });
readTheme();
renderDb();
});
})();