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Sound & Music

The wave nature of sound, Fourier analysis and acoustic phenomena. From standing waves to Chladni figures — the mathematics of what we hear.

8+ simulations Web Audio API Wave Equation · FFT

Category Simulations

Sound and wave phenomena in the browser

The wave nature of sound — sound is a pressure oscillation that propagates through a medium at ~343 m/s in air. The same wave equation describes water, light and quantum states — the mathematics is universal, only the medium differs.

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★☆☆ Beginner
2D Wave Equation
Interactive simulation of 2D waves on a surface. Click on the field — watch waves propagate, reflect and interfere. Finite-difference scheme in real time.
Wave Equation FD Scheme Canvas2D
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★☆☆ Easy
Rain & Ambient Sound
Raindrops fall and create circular ripples — each impact generates a short pressure pulse modelled as a point source of spherical waves on the water surface. Web Audio API ambient rain soundtrack included.
Web Audio Ripples Canvas 2D
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★★☆ Moderate
Ocean Waves
Gerstner trochoidal waves computed in a vertex shader. The sum of sinusoids model approximates the dispersion relation ω² = gk for deep-water gravity waves.
Gerstner Waves GLSL Dispersion
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★☆☆ Easy
Billiards & Collisions
Elastic collisions between hard discs. Sound on each impact is synthesised as a short triangular wave burst — pitch proportional to the relative impact velocity. Impulse-based collision resolution.
Impulse Collision Web Audio Canvas 2D
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★★☆ Moderate New
Chladni Figures
Sand on a metal plate forms geometric patterns at certain frequencies. Normal vibration modes, standing waves and resonance — visualising normal modes through the 2D wave equation.
Chladni Resonance Wave Audio
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★★☆ Moderate New
Fourier Synthesizer
Build complex waves from the sum of sinusoids. Watch harmonics compose into a sawtooth, square wave and arbitrary shape. Web Audio API and Canvas 2D.
Fourier Web Audio Harmonics
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★★★ Advanced New
Wave Equation
1D string and 2D membrane wave PDE solved via finite differences. Pluck the string or tap the membrane to watch standing waves, modes and interference patterns emerge in real time.
PDE Finite Differences Canvas 2D
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★★☆ Moderate
Wave Interference
Interactive wave interference and superposition. Place wave sources anywhere — watch constructive and destructive interference, Young's fringes and phase cancellation live.
Superposition Young's Fringes Canvas 2D
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★☆☆ Beginner
Doppler Effect
Visualise how a moving sound source compresses wavefronts ahead and stretches them behind. Adjust speed to hear the classic pitch shift of passing vehicles.
Canvas 2D Waves Acoustics
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★☆☆ Beginner New
String Physics — Vibrating String & Harmonics
Simulate a vibrating string with the 1D wave equation. Pluck it or excite harmonics from fundamental to the 10th overtone. Tune tension and linear density to hear and see standing waves.
Wave Equation Harmonics Canvas 2D
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★★☆ Moderate
Standing Waves
Superposition of incident and reflected waves forming standing wave patterns. Visualise nodes, antinodes and harmonics on a string or air column.
Canvas 2D Harmonics Resonance
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★★☆ Moderate New
Coupled Oscillators
Explore normal modes, beats, and energy transfer in a chain of coupled spring-mass oscillators. Excite individual modes and watch phonon-like wave packets propagate.
Normal Modes Beats Canvas 2D
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★☆☆ Easy New
Standing Waves in Pipes
Visualize acoustic standing waves in open and closed pipes. Choose harmonic mode, tube length, and sound speed. Observe displacement and pressure nodes and antinodes in real time.
Harmonics Resonance Canvas 2D

Key Concepts

The physics and mathematics behind acoustic simulation

Wave Equation
∂²u/∂t² = c²∇²u governs mechanical waves, EM waves and quantum amplitudes. The speed c = √(B/ρ) depends on bulk modulus B and density ρ of the medium.
Fourier Analysis
Any periodic signal decomposes into a sum of sinusoids (harmonics). The DFT converts N time samples to N frequency components in O(N log N) using the Cooley-Tukey FFT.
Standing Waves
Two identical waves travelling in opposite directions superpose to form nodes (zero amplitude) and antinodes (maximum amplitude). Resonant modes occur at frequencies f_n = n·c/2L.
Doppler Effect
A moving source compresses wavefronts in front (higher pitch) and stretches them behind (lower pitch). Observed frequency f′ = f·(c ± v_observer)/(c ∓ v_source).

Learning Resources

Articles about the mathematics of sound and waves

Article 2D & 3D Wave Equation Differential wave equation. Finite differences: explicit scheme. Standing waves and harmonics. → Article Fourier Transform and Sound Decomposing signals into harmonics. DFT and the Cooley-Tukey FFT algorithm. Spectrogram in the browser. → Article Gerstner Waves & GLSL Trochoidal Gerstner waves in a vertex shader. Fresnel reflections and foam on crests. →
All articles →

About Sound & Acoustics Simulations

Waves, vibration, harmonics, and resonance — made audible and visible

Sound and acoustics simulations visualise the wave physics that underlies all audio phenomena. Canvas 2D wave propagation shows circular wavefronts spreading from a point source and diffracting around obstacles. Chladni figure simulations drive a virtual plate at resonant modes and show the emergent nodal patterns. Fourier audio visualisers decompose live microphone input into harmonic components in real time.

These simulations bridge physics and music theory. Room acoustics models trace early reflections and late reverberation using image-source methods. Standing-wave resonators reveal how flute, organ pipe, and percussion instrument tones are formed. By interacting with frequency, medium density, and boundary conditions you explore the same physics studied in architectural acoustics, sonar engineering, and instrument design.

Each simulation in this category is built with accuracy and interactivity in mind. The underlying mathematical models are the same ones used in academic research and professional engineering — just made accessible through a web browser. Changing parameters in real time and observing the results is one of the most effective ways to build intuition for complex scientific and engineering concepts.

Key Concepts

Topics and algorithms you'll explore in this category

Interactive ModelReal-time browser simulation with live parameter controls
WebGL / Canvas 2DHardware-accelerated rendering in the browser
Mathematical FoundationDifferential equations and numerical integration
Open SourceMIT-licensed code — inspect, fork, and learn
No Install RequiredRuns directly in Chrome, Firefox, Safari, Edge
Educational FocusBuilt to explain the underlying science clearly

🎵 Test Your Sound Knowledge

5 questions — waves, frequency, acoustics and more

Frequently Asked Questions

Common questions about this simulation category

Do these simulations require installation?
No. Every simulation runs entirely in your web browser using WebGL and Canvas 2D. Nothing to install or download — open the page and the simulation starts immediately.
Can I use these simulations for teaching?
Yes — all simulations are designed to be educational and run without an account or login. They are widely used in university lectures, high-school science classes, and self-directed learning. Embed them via iframe or link directly.
What devices do the simulations support?
All simulations work on desktop browsers (Chrome, Firefox, Edge, Safari). Many work on mobile and tablets too, though some physics-heavy simulations benefit from the GPU performance of a desktop or laptop.

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