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Sound & Music

Explore the wave nature of sound through interactive browser simulations covering acoustics, vibration, harmonics and resonance. This category spans the phenomena that shape everything we hear: how pressure waves propagate through air and other media at roughly 343 metres per second, how standing waves form nodes and antinodes, how Fourier analysis decomposes any timbre into harmonics, and how Chladni figures, the Doppler effect and interference patterns emerge from the same wave equation. By adjusting frequency, tension, medium density and boundary conditions in real time, you can build genuine intuition for acoustic physics — the same mathematics applied in instrument design, room acoustics, ultrasound imaging and sonar engineering. Each simulation makes abstract equations audible and visible in your browser, with no installation required.

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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★★★ Advanced
Acoustic Lens — Focusing Sound
Solve the 2D wave PDE on a grid where the lens region has a different sound speed. Wavefronts bend and focus exactly where Snell's-law rays predict — the basis of ultrasound imaging.
Canvas 2D Wave PDE Refraction FDTD
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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
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★★☆ Moderate New
Auditory Scene Analysis
Bregman's ASA: auditory streaming segregates concurrent sounds into streams. Frequency proximity (ΔF...
Auditory Streaming Perception Acoustics

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

What is the difference between a standing wave and a travelling wave?
A travelling wave carries energy from one place to another — like a sound pulse moving through air. A standing wave forms when two identical waves travel in opposite directions and superpose: the result has fixed nodes (zero displacement) and antinodes (maximum displacement) that appear stationary. You can explore both in the Wave Equation and Standing Waves in Pipes simulations.
How does Fourier analysis relate to sound?
Any periodic sound waveform — a violin note, a vowel sound, a square wave — can be expressed as a sum of sinusoids (harmonics) at integer multiples of the fundamental frequency. The Fourier Synthesizer simulation lets you add harmonics one by one and hear and see how they combine into complex timbres. The DFT converts N time samples to N frequency components in O(N log N) using the FFT algorithm.
What causes Chladni figures?
When a plate is driven at a resonant frequency, it vibrates in a normal mode with nodes (zero displacement) and antinodes. Sand or salt sprinkled on the plate migrates away from vibrating antinodes and collects at the stationary nodal lines, forming the geometric Chladni patterns. Each pattern corresponds to a specific (m,n) eigenmode of the 2D wave equation on that plate geometry.
Why does the Doppler effect change pitch?
When a sound source moves toward you, each successive wavefront is emitted from a position slightly closer — so wavefronts arrive more frequently, raising the perceived frequency (pitch). The formula is f′ = f·(c ± v_observer)/(c ∓ v_source), where c ≈ 343 m/s in air. The Doppler Effect simulation visualises this wavefront compression and expansion in real time.

Other Categories

Every Sound & Acoustics simulation in this collection turns wave physics into something you can hear and see. Launch an interactive Sound & Acoustics model to watch wavefronts spread, harmonics stack into a timbre, or sand gather along the nodal lines of a vibrating plate. Because you control frequency, medium and geometry live, you can learn Sound & Acoustics online far faster than from a textbook alone. The same principles drive real-world applications such as concert-hall and architectural acoustics, noise control, loudspeaker and instrument design, ultrasound imaging and underwater sonar.