Wave equation in one dimension¶
The wave equation is a second-order linear partial differential equation used to describe the propagation of waves, including standing wave fields such as mechanical or electromagnetic waves.
Notes:
This equation is called one-dimensional because the displacement function depends only on one spatial dimension.
Links:
- displacement¶
Factor representing a displacement from rest position, which could be pressure, position, electric field, etc., as a function of position and time.
- Symbol:
u(x, t)- Latex:
\(u{\left(x,t \right)}\)
- Dimension:
any_dimension
- phase_speed¶
phase_speedof the wave.- Symbol:
v- Latex:
\(v\)
- Dimension:
velocity
- definition¶
Derivative(u(x, t), (x, 2)) = Derivative(u(x, t), (t, 2)) / v^2- Latex:
- \[\frac{\partial^{2}}{\partial x^{2}} u{\left(x,t \right)} = \frac{\frac{\partial^{2}}{\partial t^{2}} u{\left(x,t \right)}}{v^{2}}\]