wav-fourier-chladni 1.0.0

Generate Chladni plate resonant pattern signatures from WAV audio waveforms using Fourier peak frequency estimation

WAV → Fourier → Chladni Pattern

An interactive tool to analyze WAV audio files, perform discrete Fourier analysis to extract dominant peak frequencies, and map those peaks to physical resonant modes on a square Chladni vibrating plate.

For the mathematical background of plate vibration models, see this paper on Chladni Plates.

Project Structure

• voca-spectral.py — The main interactive Python pipeline script (3-step TUI: input selection, Fourier peak analysis, and visualizer exporting).
• fourier_analysis.html — Dynamic HTML report template displaying audio waveform and FFT spectrum charts (Chart.js).
• chladni_simulator.html — Interactive 2D vibrating plate simulator displaying nodal sand patterns corresponding to the wave equation.
• fourier_transform_analysis.md — Document summarizing Fourier transform calculations and eigenvalue mapping.

Features

• WAV Audio Analysis — Parse 16-bit PCM mono WAV waveforms and compute dominant peak frequencies using discrete Fourier analysis.
• Mac-Native UI Dialogs — Native macOS file picker window dialogs (osascript) for importing audio and selecting export folders, with terminal fallback prompts for Windows/Linux.
• Immediate Validation — Immediate WAV format parsing and corruption checks during step 1 before starting computation.
• Vector SVG Exports — Generate resolution-independent SVG designs of the resulting nodal sand patterns for graphic/branding usage.
• Portable Web Visualizers — Export standalone HTML dashboards to inspect audio waveforms, FFT spectra, and simulated 2D plate nodal lines.
• Zero External Python Dependencies — Built entirely on the standard Python library (no numpy/scipy/matplotlib required to run the core script).

Advanced Wave Mechanics

This project models Chladni sand patterns using Cartesian standing wave solutions of the multi-dimensional wave equation.

The Cartesian Wave Equation

For a square vibrating plate $\Omega = {(x,y) \in \mathbb{R}^2 \mid -L \le x, y \le L}$, the displacement $u(x, y, t)$ is modeled by:

$$u_{tt} = c^2\nabla^2u = c^2\left(\frac{\partial^2u}{\partial x^2} + \frac{\partial^2u}{\partial y^2}\right)$$

Assuming clamped boundary conditions at the edges, the standing wave solutions (eigenmodes) can be approximated by:

$$u(x, y, t) = \sum_{n=1}^{\infty}\sum_{m=1}^{\infty} w_{nm} \cdot \left(\sin\left(\frac{n\pi x}{L}\right)\sin\left(\frac{m\pi y}{L}\right) + \beta\sin\left(\frac{m\pi x}{L}\right)\sin\left(\frac{n\pi y}{L}\right)\right)\cos(\omega_{nm} t)$$

Where:

• $n, m$ are the integer mode parameters (eigenvalues).
• $w_{nm}$ is the weight of each mode, mapped directly from the dominant audio frequency amplitudes computed via Fourier analysis.
• $\beta$ is the symmetry factor (typically $\pm 1$ for square plates).
• The sand particles accumulate at the nodal lines where the plate displacement is zero, i.e., $u(x,y,t) \approx 0$.

---

Installation & Running

Since the core pipeline runs entirely on the Python standard library, there are no third-party Python libraries to install.

1. Install via pip

You can install the package directly as a global CLI tool from the repository folder:

pip install .

Once installed, you can launch the pipeline from anywhere using the global command:

wav-fourier-chladni

2. Alternative: Run the source script directly

If you do not want to install it globally, you can execute the script directly from the source directory:

python3 wav_fourier_chladni/cli.py

3. Prerequisites (Optional)

To run the core analysis and visualizers, you only need Python 3 installed.

If you wish to use the live microphone recording feature:

• macOS: brew install sox or ensure ffmpeg is in your system path.
• Linux: sudo apt install alsa-utils (for arecord) or sox.

The script will guide you through:

1. Audio Selection: Pick a WAV file using a native macOS window picker or record live from the microphone.
2. Analysis: Performs the discrete Fourier calculations.
3. Resonant Signatures: Renders an ASCII art preview of the pattern in the terminal, and lets you choose to export SVG files or HTML dashboards.

🤝 Contributing

Got ideas? Found a bug?

PRs and issues are very welcome! This is a community tool and it gets better when more people chip in. Even small improvements — better selectors, new step actions, docs fixes — make a real difference.

Open an issue or just submit a PR. Let's build it together. 🙌

---

📄 License

MIT

---

_{Built by Ganidhu and Baymax}