Impedance is defined for mechanical systems as
force divided by velocity, while the inverse (velocity/force) is
called an admittance. For dynamic systems, the impedance of a
``driving point'' is defined for each frequency
, so that the
``force'' in the definition of impedance is best thought of as the
peak amplitude of a sinusoidal applied force, and similarly for the
velocity. Thus, if
denotes the Fourier transform of the
applied force at a driving point, and
is the Fourier
transform of the resulting velocity of the driving point, then the
driving-point impedance is given by
In the lossless case (no dashpots, only masses and springs), all driving-point impedances are purely imaginary, and a purely imaginary impedance is called a reactance. A purely imaginary admittance is called a susceptance. The term immittance refers to either an impedance or an admittance [35]. In mechanics, force is typically in units of newtons (kilograms times meters per second squared) and velocity is in meters per second.
In acoustics [320,321], force takes the form of
pressure
(e.g., in physical units of newtons per meter squared),
and velocity may be either particle velocity in open air
(meters per second) or volume velocity in acoustic tubes
(meters cubed per second) (see §B.7.1 for
definitions).
The wave impedance (also called the characteristic
impedance) in open air is the ratio of pressure to particle velocity
in a sound wave traveling through air, and it is given by
, where
is the density (mass
per unit volume) of air,
is the speed of sound propagation,
is ambient pressure, and
is the ratio of the specific
heat of air at constant pressure to that at constant volume. In a
vibrating string, the wave impedance is given by
, where
is string density (mass per unit length) and
is
the tension of the string (stretching force), as discussed further in
§C.1 and §B.5.2.
In circuit theory [110], force takes the form of electric
potential in volts, and velocity manifests as electric current in amperes
(coulombs per second). In an electric transmission line, the
characteristic impedance is given by
, where
and
are the inductance and capacitance, respectively, per unit length along the
transmission line. In free space, the wave impedance for light is
, where
denotes the speed of light,
and
and
are
the permeability and permittivity, respectively, of free space. One might
be led from this to believe that there must exist a medium, or ``ether'',
which sustains wave propagation in free space; however, this is one
instance in which ``obvious'' predictions from theory turn out to be wrong
(see the special theory of relativity for details).