Wave Equation in 1D and 2D 1D Wave Equation: The 1D wave equation describes the propagation of a disturbance or wave in a one-dimensional space with a c...
Wave Equation in 1D and 2D
1D Wave Equation:
The 1D wave equation describes the propagation of a disturbance or wave in a one-dimensional space with a constant speed. The general wave equation in 1D is:
∂²u/∂t² = v² ∂²u/∂x²
where:
u(x, t) is the displacement or wave function at position x and time t
v is the wave speed
x is the spatial coordinate
t is the temporal coordinate
2D Wave Equation:
The 2D wave equation describes the propagation of a disturbance or wave in a two-dimensional space with a constant speed. The general wave equation in 2D is:
∂²u/∂t² = v² (∂²u/∂x² + ∂²u/∂y²)
where:
u(x, y, t) is the displacement or wave function at position (x, y) and time t
v is the wave speed
x and y are the spatial coordinates
Examples:
1D Wave Equation:
2D Wave Equation: