# Plane wave > On the **[[PORTAL_Acoustics|Acoustics]]** vibration spine · article face [[Acoustics]]. Microsim first, then the physics. ## Microsims — p5.js <div class="microsim-player"> <iframe src="https://editor.p5js.org/sciencenibber/full/YWAQ06VnR" width="100%" height="620" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Plane wave — p5.js microsim"></iframe> </div> <div class="microsim-fallback"><em>Live p5.js microsim (desktop) · <a href="https://editor.p5js.org/sciencenibber/sketches/YWAQ06VnR">open / fork the sketch in the p5.js editor</a></em></div> **Plane wave (p5.js).** A two-panel anatomy of the plane-wave idealization, both views driven by the same scalar field p(x, y, t) = P0 * cos(kx*x + ky*y - omega*t). The left panel rasterises a 1.5 m square slice of medium as a blue-to-black-to-amber pressure colour map; the bright bands are crests, dark bands are troughs, and the bands themselves are the wavefronts — perpendicular to the white wavevector arrow. The right panel scrolls a microphone-style [[Time_series|time series]] at the centre probe r0, with a magenta bracket marking one period T. Sliders for f, P0, c, and theta let the reader rotate the wavevector, watch lambda = c / f live, and hear an audio-gated sine tone at the slider frequency. ## Overview A plane wave is a [[Wave|wave]] whose surfaces of constant phase — its wavefronts — are infinite parallel planes oriented perpendicular to the direction of propagation. Unlike a spherical wave radiating from a point source, every cross section of a plane wave carries the same amplitude and the same instantaneous phase, so the pressure (or displacement) depends only on a single spatial coordinate measured along the propagation axis. The canonical scalar form is p(r, t) = P0 * cos(k . r - omega * t), with wavevector k = (2 * pi / lambda) * n_hat pointing along the direction of travel, [[Angular_frequency|angular frequency]] omega = 2 * pi * f, and phase speed c = omega / k = f * lambda. Plane waves are an idealization — no compact source actually produces one — but they are the indispensable building blocks of acoustic and electromagnetic theory, because any well-behaved field can be decomposed into a superposition of plane waves (the spatial Fourier transform). In acoustics they are the natural mode of propagation inside a long duct below cutoff, the asymptotic far field of any compact source, and the cleanest framework in which reflection, refraction across a [[Sound|sound]]-speed jump, and transmission through layered media are written. The plane wave is the workhorse abstraction every later Audio article quietly uses. ## On the Acoustics spine Neighbours on the vibration spine: [[Sound]] · [[Wave]] · [[Oscillation]] · [[Vibration]] · [[Acoustic_wave]] · [[Mechanical_wave]]. Bridge portal [[PORTAL_Acoustics]] · index [[PORTAL_INDEX]] · systems root [[PORTAL_Systems]]. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Plane_wave) : [Wikitube](https://en.wikitube.io/wiki/Plane_wave) --- *Repopulated 2026-08-05 · microsim-first transfer from legacy GENERATIVE lane · p5 sciencenibber/YWAQ06VnR · 0 deletions.*