43:["$","title",null,{"children":"Room modes in a rectangular room | The Audio Stuff | Observable"}] 4b:[] 47:{"id":"ab24637da094ca11","slug":"room-modes-in-a-rectangular-room","title":"Room modes in a rectangular room","thumbnail":"f6a2d8703f1b8307d2950f375a9a418e2a3453c5e7175c17df22be502aca25d1","access_level":"public","create_time":"$D2026-10-21T12:49:23.235Z","update_time":"$D2026-10-22T18:31:10.438Z","view_time":null,"first_public_time":"$D2026-10-22T15:48:41.722Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"54b6686623fffd32","login":"theaudiostuff","name":"The Audio Stuff","avatar_url":null,"tier":"free_2026","bio":"The Audio Stuff: independent reviews of headphones, speakers and DACs, plus 16 free browser tools, including headphone amp power matching, room modes and ABX blind testing. https://theaudiostuff.com/tools/","followed_by_you":false,"follows_you":false},"version":18,"publish_version":18,"role":null,"authored":false,"authors":[{"type":"individual","id":"f09ab9b9e133cbb5","login":"theaudiostuff","name":"The Audio Stuff","avatar_url":null,"tier":null,"bio":"The Audio Stuff: independent reviews of headphones, speakers and DACs, plus 16 free browser tools, including headphone amp power matching, room modes and ABX blind testing. https://theaudiostuff.com/tools/","followed_by_you":false,"follows_you":false}],"members":[{"type":"team","id":"54b6686623fffd32","login":"theaudiostuff","name":"The Audio Stuff","avatar_url":null,"tier":"free_2026","role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"titling":"auto","title":"Room modes in a rectangular room","cells":[{"id":1,"value":"# Room modes in a rectangular room\n\nA room mode is a frequency where sound bouncing between two parallel surfaces reinforces itself. In a small room these standing waves are the main reason bass sounds boomy at one seat and thin at another.\n\nFor an **axial** mode between two parallel walls a distance *L* apart, the frequencies are\n\n*f* = *n* × *c* ÷ (2 × *L*), with *n* = 1, 2, 3…\n\nwhere *c* ≈ 343 m/s is the speed of sound at about 20 °C. A 4.5 m wall-to-wall distance gives modes at about 38, 76, 114 and 152 Hz.\n\nSet the room size below to see where the axial modes of each dimension land, and where modes from different dimensions bunch together. Bunched modes stack into one strong boom; evenly spread modes sound smoother.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2,"value":"const length = view(Inputs.range([2, 15], {label: \"Length (m)\", step: 0.05, value: 5}));\nconst width = view(Inputs.range([2, 15], {label: \"Width (m)\", step: 0.05, value: 4}));\nconst height = view(Inputs.range([2, 5], {label: \"Height (m)\", step: 0.05, value: 2.5}));","pinned":true,"hidden":false,"mode":"ts","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3,"value":"// Axial modes up to 300 Hz for each room dimension\nconst c = 343; // speed of sound in m/s at about 20 °C\nconst modes = [[\"Length\", length], [\"Width\", width], [\"Height\", height]]\n .flatMap(([dimension, d]) => d3.range(1, 20).map((n) => ({dimension, n, f: (n * c) / (2 * d)})))\n .filter((m) => m.f <= 300)\n .sort((a, b) => a.f - b.f);","pinned":true,"hidden":false,"mode":"ts","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":4,"value":"Plot.plot({\n title: \"Axial room modes by dimension\",\n marginLeft: 60,\n height: 200,\n x: {label: \"Frequency (Hz)\", domain: [0, 300], grid: true},\n y: {label: null, domain: [\"Length\", \"Width\", \"Height\"]},\n color: {domain: [\"Length\", \"Width\", \"Height\"]},\n marks: [\n Plot.tickX(modes, {x: \"f\", y: \"dimension\", stroke: \"dimension\", strokeWidth: 2, channels: {n: \"n\"}, tip: {format: {x: (x) => x.toFixed(1) + \" Hz\"}}})\n ]\n})","pinned":true,"hidden":false,"mode":"ts","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"// Pairs of modes from different dimensions within 5% of each other: likely pile-ups\nconst pileUps = modes.flatMap((a, i) =>\n modes.slice(i + 1)\n .filter((b) => b.dimension !== a.dimension && Math.abs(b.f - a.f) / a.f < 0.05)\n .map((b) => `${a.dimension} ${a.n} (${a.f.toFixed(0)} Hz) and ${b.dimension} ${b.n} (${b.f.toFixed(0)} Hz)`)\n);\ndisplay(pileUps.length\n ? html`

Possible pile-ups: ${pileUps.join(\"; \")}.

`\n : html`

No modes from different dimensions fall within 5% of each other below 300 Hz.

`);","pinned":true,"hidden":false,"mode":"ts","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":6,"value":"Inputs.table(\n modes.map((m) => ({Dimension: m.dimension, Order: m.n, \"Frequency (Hz)\": +m.f.toFixed(1)})),\n {sort: \"Frequency (Hz)\"}\n)","pinned":true,"hidden":false,"mode":"ts","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":7,"value":"html`

This notebook covers axial modes only, which are usually the strongest. Tangential and oblique modes add more, weaker resonances, and real rooms are rarely perfect boxes.

I make a free room mode calculator that also covers tangential and oblique modes, L-shaped, round and arched-ceiling rooms, and adds a 3D pressure view. It is one of the free tools at The Audio Stuff, needs no account and runs in your browser.

Jakub Charkiewicz, The Audio Stuff

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