Wave equation

The wave equation is an important differential relationship in physics. It describes how waves propagate through mediums, whether they be [transverse waves] (e.g. electromagnetic radiation) or [longitudinal waves] (e.g. sound waves).

One-Dimensional Wave Equation

One type of wave equation is the one-dimensional wave equation. The mathematical relation describes a wave whose parts only oscillate in one dimension. This wave, however, can propagate in all three spacial dimensions. An example would be a vibrating rope or string with both ends fixed.

The one-dimensional wave equation can be written:

${\frac {\partial ^{2}y}{dx^{2}}}={\frac {1}{v^{2}}}{\frac {\partial ^{2}y}{dt^{2}}}$

where y = y(x,t), the y-direction of motion at a point x that changes with time t, and v = the phase velocity of the wave.