The wave equation is a mathematical description governing the PROPAGATION of waves. For the string, for example, the wave equation takes the form
in terms of the transverse displacement of the string, .
For one-dimensional waves in air it takes the form
in terms of the ACOUSTIC PRESSURE p(x,t).
These equations are partial differential equations (PDEs), because they involve partial derivatives in terms of both the variables x and t. They are second order PDEs.