π
Wave Equation Explorer
π Help / Theory
Wave Speed
c (wave speed)
1.00
Initial Condition
u(x,0) shape
Gaussian
Sine Mode
Square Pulse
Triangle
Two Pulses
Initial velocity ut(x,0)
Zero (standing)
Rightward pulse
Leftward pulse
Amplitude A
1.0
Width Ο
0.08
Numerical Setup
Grid N
300
CFL Ξ½
0.90
Boundary Conditions
Type
Periodic
Dirichlet (u=0 walls)
Neumann (free ends)
Absorbing (one-way)
Display
Total u(x,t)
Exact (d'Alembert)
Right-traveling f(xβct)
Left-traveling g(x+ct)
Initial profile
Fill under curve
Animation
Speed
0.1
Γ
Loop at T
6.0
Live Stats
Energy E:
β
KE / PE:
β
LΒ² error:
β
max|u|:
β
π Evolution
π xβt Diagram
β‘ Energy
π΅ Normal Modes
βΆ Play
β Step
βΊ Reset
t = 0.000
Ξ½ = 0.90
u(x, t) = f(xβct) + g(x+ct)
βu/βt β Velocity field
xβt Spacetime β Characteristics at slope Β±1/c
Total energy E(t) = KE + PE (should be conserved)
Normal mode decomposition β select a mode below
t = 0.000
CFL = β
E = β
LΒ² = β
Periodic
π Wave Equation β Theory & Resources
Γ