What is the Wave Lab multi-solver?

Wave Lab is a guided workflow that chains 5 individual PolySim solvers into one end-to-end analysis, piping each result into the next step.

Yes. Every step runs entirely in your browser using real numerics — no install, no account, no cloud cost. Custom or private solver packs are available as a paid service.

Physics & Quantum Pack · Multi-Solver

Wave Lab

Interference to FFT. This multi-solver chains 5 solvers into a single guided workflow — run each step in order and carry the result forward.

Workflow steps

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Wave Interference

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Wave Interference StudioLive

two-source interference · ripple tank

Controls

Speed1×

Two point sources emit circular waves — where they meet, you see constructive and destructive interference fringes. Drag either source on the canvas to reposition it and watch the pattern update live.

Presets

Frequency

Source separation

▶ Run in Python

Data Inspector

Sources2

Grid220×220

Wavelength15.7 px

Separation100 px

Patterninterference fringes

Governing equation

y = A_{1} sin (k r_{1} - ω t) + A_{2} sin (k r_{2} - ω t), Δ r = mλ, λ \approx 15.7 px, Δ s = 100 px

Reading this result: Wavelength is about 15.7 px and the two sources sit 100 px apart. Bright fringes appear where the path difference to the two sources equals a whole number of wavelengths (constructive interference); dark fringes fall halfway between, where the difference is a half-wavelength (destructive interference). Shrinking the wavelength or widening the separation would pack more fringes into the same space.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Standing Waves

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Standing Waves on a StringLive

harmonics · nodes & antinodes

Controls

Speed1×

A string fixed at both ends can only vibrate at its harmonics. Each mode n has n+1 nodes (pink) that stay still while the antinodes swing — the physics of every stringed instrument.

Presets

Harmonic n

Fundamental (Hz)

Amplitude (cm)

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Data Inspector

Harmonicn = 3

Frequency330 Hz

Nodes4

Antinodes3

Wavelength2L/3

Governing equation

y = 2 A sin (k x) cos (ω t), f_{3} = \frac{3 v}{2 L} = 330 Hz

Reading this result: 3 half-wavelengths fit the string, so there are 3 antinodes (max swing) and 4 nodes (fixed points). At harmonic n = 3 the string sings at 330 Hz — exactly 3× the 110 Hz fundamental, and the wavelength is 2L/3.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Doppler

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Doppler EffectLive

moving source · wavefront compression

Controls

Speed1×

A moving source squeezes its wavefronts ahead and stretches them behind — higher pitch approaching, lower pitch receding. Push past the wave speed for a sonic boom.

Presets

Source speed

Source frequency (Hz)

▶ Run in Python

Data Inspector

Mach number0.68

Regimesubsonic

Source freq440 Hz

Approaching f'1383 Hz

Receding f'262 Hz

Governing equation

f^{'} = f \frac{c \pm v _{o}}{c \mp v _{s}} = 440 \cdot \frac{2.2}{2.2 \mp 1.5} = 1383 / 262 Hz

Reading this result: Approaching, the 440 Hz source is heard higher — about 1383 Hz; receding, it drops to about 262 Hz. The faster the source (Mach 0.68), the wider that split.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Beats

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Beats & SuperpositionLive

two close frequencies interfere

Controls

Two tones close in frequency add to a wave whose amplitude throbs at the difference frequency — the beats a musician hears when tuning.

Presets

Frequency 1

Frequency 2

▶ Run in Python

Data Inspector

f₁, f₂10, 11

Beat frequency1.0

Effectamplitude throb

Governing equation

f_{beat} = ∣ f_{2} - f_{1} ∣ = ∣11 - 10∣ = 1.0 Hz

Reading this result: At a 1.0 Hz beat the throb is too fast to count as a pulse; the ear stops hearing separate beats and instead hears roughness or dissonance around the 10.5 Hz average pitch.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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FFT

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Fourier Transform (FFT)Live

decompose a signal into frequencies

Controls

Build a signal from a few sine tones plus noise, and the discrete Fourier transform recovers exactly which frequencies are present — the foundation of all signal processing.

Presets

Tone 1 frequency

Tone 2 frequency

Tone 3 frequency

Noise

▶ Run in Python

Data Inspector

Samples256

Peaks at4, 9

TransformDFT

Governing equation

X_{k} = n = 0 \sum N - 1 x_{n} e^{- 2 π ik n / N} (N = 256, O (N lo g N))

Reading this result: The FFT splits this 2-tone signal into bins: each input sinusoid at 4, 9 appears as a distinct spike, and with noise at 0 the baseline between them stays clean.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Frequently asked questions

What is the Wave Lab multi-solver?: Wave Lab is a guided workflow that chains 5 individual PolySim solvers into one end-to-end analysis, piping each result into the next step.
Is it free to use?: Yes. Every step runs entirely in your browser using real numerics — no install, no account, no cloud cost. Custom or private solver packs are available as a paid service.