Movies for the One-Dimensional Wave Equation:   utt = uxx  

Splitting of waves

            

 

 

Interaction of waves

            

 

 

Particles and waves

The wave solution u(t,x) = cos t sin x = (sin(x-t) + sin(x+t))/2
Constitutent traveling waves (particles)
Particles and Waves

 

 

Error Function Solution

            

 

 

Forcing and resonance

Periodic solution Quasiperiodic solution
Resonant solution

 

 

Dirichlet boundary conditions

            

 

 

Odd periodic extension

            

 

 

Plucked string

Dirichlet boundary conditions
Neumann boundary conditions

 

 

Hammer blow

            
Dirichlet boundary conditions Neumann boundary conditions