Wave Packet & Dispersion

This interactive simulator explores Wave Packet & Dispersion in Waves & Sound. Superpose cos(kx−ωt); ω=ck+αk²; spreading vs Wave on String PDE. Use the controls to change the scenario; watch the visualization and any graphs or readouts to connect the model with lectures, labs, and homework.

Who it's for: Best once you already know the basic definitions and want to build intuition. Typical context: Waves & Sound.

Key terms

  • wave
  • packet
  • dispersion
  • wave packet dispersion
  • waves
  • sound

Live graphs

How it works

**Wave on a String** in this lab solves a damped wave PDE with a driven boundary — good for propagation and reflections. This page instead builds a **packet** as a sum of sinusoids with a **dispersion relation** ω(k). When ω is linear in k (α = 0), the envelope travels unchanged; with **α ≠ 0**, components walk out of phase and the packet **disperses**.

Key equations

η(x,t) = Σₙ Aₙ cos(kₙx − ω(kₙ)t), ω(k) = ck + αk²
v_p = ω/k, v_g = dω/dk = c + 2αk