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Using the above identities, we have that the force distribution along
the string is given in terms of velocity waves by

(C.44) 
where
. This is a fundamental
quantity known as the wave impedance of the string (also called
the characteristic impedance), denoted as

(C.45) 
The wave impedance can be seen as the geometric mean of the two
resistances to displacement: tension (spring force) and mass (inertial
force).
The digitized traveling forcewave components become

(C.46) 
which gives us that the rightgoing force wave equals the wave
impedance times the rightgoing velocity wave, and the leftgoing
force wave equals
minus the wave impedance times the leftgoing velocity wave.^{C.4}Thus, in a traveling wave, force is always in phase with
velocity (considering the minus sign in the leftgoing case to be
associated with the direction of travel rather than a
degrees
phase shift between force and velocity). Note also that if the
leftgoing force wave were defined as the string force acting to the
left, the minus sign would disappear. The fundamental relation
is sometimes referred to as the mechanical counterpart of
Ohm's law for traveling waves, and
in c.g.s. units
can be called acoustical ohms [263].
In the case of the acoustic tube [320,299], we have the
analogous relations

(C.47) 
where
is the rightgoing traveling longitudinal pressure
wave component,
is the leftgoing pressure wave, and
are the left and rightgoing volume velocity waves. In the acoustic
tube context, the wave impedance is given by

(C.48) 
where
is the mass per unit volume of air,
is sound speed in
air, and
is the crosssectional area of the tube.
Note that if we had chosen particle velocity rather than volume
velocity, the wave impedance would be
instead, the wave
impedance in open air. Particle velocity is appropriate in open air,
while volume velocity is the conserved quantity in acoustic tubes or
``ducts'' of varying crosssectional area.
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