Description
Superposition of standing-wave modes in a cavity of length L = 1 m, illustrating the pattern resulting from the sum y(x, t) = A·Σ (from n₀ to n_f) sin(kₙx)sin(ωₙt), with ωₙ = πvn/L and kₙ = ωₙ/v. In the Single mode position, only mode n₀ is simulated (n_f = n₀); in the Multimode position, modes n₀ through n_f are superposed.
Controls
Click the graph or Start to start/pause the animation; Shift-click or Restart resets the simulation. Switch between Single mode and Multimode to choose whether only mode n₀ or the superposition from n₀ through n_f is displayed.
Physical model
Each mode n corresponds to a harmonic with frequency ωₙ proportional to n; the superposition of several modes (multimode) illustrates how a more complex waveform can be constructed by summing simple standing-wave modes—the same idea behind Fourier analysis.
Developers
Marco P. M. de Souza
References
H. Moysés Nussenzveig, Curso de Física Básica: Fluidos, Oscilações e Ondas, Calor (Blucher, 2014).