Educational Longitudinal Wave Simulator: Standing Waves, Reflection, and Damping

Web-Based Longitudinal Wave Simulator: From Pulse to Continuous Wave

What it is

A web app that models longitudinal (compressional) waves in one dimension, letting users generate short pulses or continuous sinusoidal sources and observe resulting pressure, displacement, and particle velocity over time.

Key features

• Pulse and continuous sources: send single pulses, Gaussian pulses, or steady sinusoidal driving at one or both ends.
• Adjustable parameters: wavelength/frequency, amplitude, pulse width, medium density, bulk modulus (or sound speed), damping/viscosity, boundary conditions (fixed, free, absorbing).
• Real-time plots & animation: animated particle positions (or slices) and synchronized graphs of pressure, displacement, and velocity vs. position and vs. time.
• Energy diagnostics: instantaneous and cumulative kinetic/potential energy, transmission/reflection coefficients at impedance mismatches.
• Interactive measurement tools: pick points to display time series, measure wavelength, period, phase shift, and group velocity.
• Modes & scenarios: standing waves in a cavity, reflection from impedance steps, superposition of pulses, dispersion (optional numeric models).
• Export & share: save parameter sets, export data/CSV, download animation frames or GIF.

How it works (short)

Numerical solution of the 1D linear wave equation for pressure or displacement using finite-difference time-domain (FDTD) or staggered-grid (leapfrog) scheme. Boundary conditions implemented via ghost cells or perfectly matched layers (PML) for absorption. Time step limited by CFL stability condition: Δt ≤ Δx / c.

Educational uses

• Demonstrate reflection/transmission at impedance contrasts.
• Visualize standing wave nodes/antinodes and resonance.
• Explore effect of damping on pulse shape and energy loss.
• Compare pulse propagation vs. continuous wave steady-state.

Implementation notes (for developers)

• Use HTML5 canvas or WebGL for smooth animation; D3 or Plotly for synchronized graphs.
• Compute on main thread for simple grids; use Web Workers or GPU (WebGL/compute shaders) for large grids or real-time parameter changes.
• Store presets and CSV export in-browser (IndexedDB) or let users download files.
• Ensure numerical stability: enforce CFL, use second-order accurate spatial derivatives and leapfrog time integration.

Example user flow

1. Select medium (air/water/custom) and grid resolution.
2. Choose source type: pulse (Gaussian, width) or continuous (frequency, amplitude).
3. Run simulation; use sliders to change damping or frequency live.
4. Place probes to record time series; export CSV.