WaveEquation-d'Alambert'sFormula
- Author:
- Will Le
The one-dimensional wave equation for wave function u(t, x) is .
Using subscript to denote partial differentiation, we have the equation with initial conditions at t = 0: the initial waveform and the intial velocity waveform .
Jean le Rond d'Alembert has shown that the solution for this equation can be separated into two waveform-invariant waves sliding in opposite directions:
, where
, and
.
In the applet above, check "Split wave" to split u(t, x) into and .