Standing Waves and Resonance Simulation
This interactive physics simulation numerically solves the damped one-dimensional wave equation for a string driven at one end and fixed at the other, using an explicit finite-difference (Verlet-style) scheme with adaptive substepping for numerical stability. Users can adjust tension and linear density โ which together set the wave speed v = โ(T/ฮผ) โ as well as the driving frequency and amplitude, to explore how standing waves and resonance arise when the driving frequency matches one of the string's harmonic frequencies f_n = nยทv/(2L).
Live visualizations include the amplitude envelope showing node and antinode positions, the driven-end signal over time, and a harmonic series scan indicating how close the current driving frequency is to each resonant mode. This tool is designed to support physics education topics including wave mechanics, oscillations, acoustics, and resonance phenomena.
Keywords: standing wave simulation, resonance physics demo, wave equation solver, harmonic series, nodes and antinodes, string vibration simulation, physics education tool, wave speed tension density