Equations · equation
Wave Equation
Acoustics · 1746
- Equation
- ∂²u/∂t² = c²·∇²u
- Field
- Acoustics
- Named After
- Jean le Rond d'Alembert
- Year
- 1746
Symbols
u the disturbance (string displacement, air pressure, field strength) · t time · c wave speed · ∇² Laplacian (spatial curvature of the disturbance)
Significance
One equation for everything that waves: a plucked string, sound in air, ripples on water — and, a century later, Maxwell found light obeying the very same form. Derived by d'Alembert for the vibrating string, it is the mathematical definition of what a wave is.
Referenced by
equation
theory
Open on the Equations shelf — the interactive card, the filters, and everything alongside it.