Mathematically, a specific acoustic impedance Zi is defined on some cross section as the ratio between the acoustic pressure p and the acoustic velocity perpendicular to the area (the normal velocity)

Here Zi is the acoustic input impedance of the external domain and it has the unit of a specific acoustic impedance. The specific acoustic impedance Zi (SI unit: Pa·s/m) is related to the acoustic impedance Zac (ratio of pressure and flow rate, SI unit: Pa·s/m3) and the mechanical impedance Zmech (ratio of force and velocity, SI unit: N·s/m) via the area A of the boundary, according to

Impedance boundary conditions only relate the normal velocity (the velocity perpendicular to the boundary) to the pressure, but do not consider the tangential velocity (component parallel to the boundary). This is due to the mathematical construction of the governing equation and the fact that pressure acoustics solves only for the scalar pressure. Put differently, the impedance boundary condition only applies to the normal component of the incident field. Thus, by applying an impedance boundary condition this tangential velocity component is ignored altogether. For this reason, impedance boundary conditions are in most cases low-order approximations to the actual boundary properties. In cases where this is unacceptable, it is consequently better to either model the boundary explicitly or use a higher-order model, such as for instance the Plane Wave Radiation at an open boundary.