# Sine wave
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## Microsims — p5.js
### Sine wave (p5.js) · `A sin(ωt+φ)`
<div class="microsim-player">
<iframe src="https://editor.p5js.org/sciencenibber/full/tNdeZlofd" width="100%" height="480" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Sine wave — p5.js microsim"></iframe>
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*The pure single-frequency tone — the atom out of which Fourier builds every other signal.*
**Open in the editor:** [▶ fork this sketch](https://editor.p5js.org/sciencenibber/sketches/tNdeZlofd) · movement *IX · Foundations & the rest of the toolbox* · library `p5js`
### Related microsims
Live sims on neighbouring articles — 5 of them inside this article's own Wikipedia link tree:
- [[Decibel]] *(in tree)*
- [[Fourier_analysis]] *(in tree)*
- [[Frequency_response]] *(in tree)*
- [[Least-squares_spectral_analysis]] *(in tree)*
- [[Wave_equation]] *(in tree)*
- [[Analog_signal]]
*Sim hosted off-article; the article owns the reference, not the runtime (WIKI_RULES §10.4). Placed by `g08_place_microsims.py`.*
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## Links (Wikipedia order)
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`Acoustics` · `Amplitude` · [[Angular_frequency]] · `Circle` · `Constant_of_integration` · `Cutoff_frequency` · `Decade_(log_scale)` · [[Decibel]] · `Derivative` · `Differentiator` · `Dot_product` · [[Engineering]] · `Euler's_formula` · `Field_(physics)` · [[Fourier_analysis]] · `Fourier_series` · `Fourier_transform` · `Frequency` · [[Frequency_response]] · `Fundamental_frequency` · `Gain_(electronics)` · `Harmonic` · `Harmonic_analysis` · `Harmonic_series_(mathematics)` · `Harmonic_series_(music)` · `Helmholtz_equation` · `High-pass_filter` · `In-phase_and_quadrature_components` · `Integral` · `Integrator` · `Joseph_Fourier` · `Lambda` · [[Least-squares_spectral_analysis]] · `Light` · `Linear_combination` · `Low-pass_filter` · `Mathematics` · `Mechanics` · `Monochromatic_radiation` · `Motion` · `Oscilloscope` · `Passband` · `Periodic_function` · `Phase_(waves)` · `Phase_velocity` · `Phasor` · [[Physics]] · `Pitch_(music)` · `Plane_wave` · `Pulse_wave` · `Pure_tone` · `Radian` · `Real_number` · `Rotation` · `Sawtooth_wave` · [[Signal_processing]] · [[Simple_harmonic_motion]] · `Sinusoidal_plane_wave` · `Sound` · `Square_wave_(waveform)` · `Standing_wave` · `Stopband` · `Superposition_principle` · `Tilde` · `Timbre` · `Time` · [[Time_series]] · `Triangle_wave` · `Turn_(angle)` · [[Wave_equation]] · `Waveform` · `Wavelength` · `Wind_wave` · `Zeros_and_poles`
> Signal Processing concept · part of the Signal Processing Portal · movement IX · !09 解析 kaiseki.svg
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*Rendered from the live microsim (▶ motion).*
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## See it next
[](Waveform)
*→ Waveform*
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## Gallery (beauty pass)
*A mass on a spring: its displacement over time is exactly a sine wave — simple harmonic motion, the mechanical face of the sinusoid. Source: Wikimedia Commons. [Details & license](https://commons.wikimedia.org/wiki/File:Animated-mass-spring.gif)*
!波 wave spintronics.svg
*波 (wave) — Wikitube hero kanji, spintronics reading. MTN / Wikitube.io original · CC BY-SA 4.0*
!波 wave physics.svg
*波 (wave) — Wikitube hero kanji, physics reading. MTN / Wikitube.io original · CC BY-SA 4.0*
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---
Back to Signal Processing Portal · the room · Semiotic gateway
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## From the Real GENERATIVE library
*Animated: Sine wave — placed from the Real G.E.N.E.R.A.T.I.V.E. course library (Audio room). Source: Wikimedia Commons (via Wikipedia article media). [Details & license](https://commons.wikimedia.org/wiki/File:One_positive_frequency_component%2C_cosine_and_sine%2C_from_rotating_vector_%28fast_animation%29.gif).*
> A sine wave, sinusoidal wave, or sinusoid (symbol: ∿) is a periodic wave whose waveform (shape) is the trigonometric sine function. In mechanics, as a linear motion over time, this is simple harmonic motion; as rotation, it corresponds to uniform circular motion. ([Wikipedia](https://en.wikipedia.org/wiki/Sine_wave))
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## Media (PD/CC)
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!Gif Library/Sine wave/One positive frequency component, cosine and sine, from rotating vector (fast animation).gif
*One_positive_frequency_component,_cosine_and_sine,_from_rotating_vector_(fast_animation).gif · Ohgddfp · CC BY-SA 4.0 · [source](https://commons.wikimedia.org/wiki/File:One_positive_frequency_component,_cosine_and_sine,_from_rotating_vector_(fast_animation).gif)*
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## What it is
A sine wave (sinusoid) is a smooth, periodic oscillation described by the sine function, characterized by a single amplitude, frequency, and phase.
## How it works / why it matters
A continuous sinusoid has the form $x(t) = A\sin(2\pi f t + \phi)$, where $A$ is amplitude, $f$ frequency, and $\phi$ phase. Sinusoids are fundamental because they are the eigenfunctions of linear time-invariant systems — passing a sinusoid through such a system changes only its amplitude and phase, not its frequency. [[Fourier_analysis|Fourier analysis]] exploits this by decomposing any signal into a sum of sinusoids, making the sine wave the basic building block of [[Frequency_domain|frequency-domain]] analysis.
The same curve appears wherever oscillation is simplest ([Wikipedia: Sine wave](https://en.wikipedia.org/wiki/Sine_wave)): traced as a linear motion over time it is simple harmonic motion — the mass-on-a-spring oscillation animated in the gallery below — and read as rotation it corresponds to uniform circular motion, which is why the projection of a spinning vector (the rotating-vector animation above) draws a sine. The waveform even carries its own symbol, ∿. In audio work a lone sinusoid is heard as a single steady pure tone with no overtones — unsourced this pass.
## Signs & universals
Instantiates: signal · frequency — an elementary periodic signal defined by a single frequency.
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> 🔣 **Shared sign-systems** — the semiotic threads this room weaves into the rest of the Wikitube (each opens its sign-system page; the number is how many rooms that notation bridges): kanji radicals (19) · circuit symbols iec (18) · acoustic diagrams (11) · peirce sign classes (10) · chart glyph dictionary (9) · morse code (5). Edges of the **semiotic spine** · index: SEMIOTICS PORTAL.
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## Related
It is the simplest Waveform and the eigenfunction of a [[Linear_time-invariant_system]], forming the basis of the Discrete Fourier transform. Sinusoids are typically represented as Continuous-time signals or sampled Discrete-time signals and serve as carrier and test signals throughout Signal Processing.
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*Built to the [[WT!P5_js_Microsim_Master_Class|p5.js Master Class]].*
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## Wikipedia : Wikitube
**Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Sine_wave) : [Wikitube](https://en.wikitube.io/wiki/Sine_wave)
## Previous hub tags
Tree parent: [[Feedback]].
Legacy hubs: none.
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*Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order).*