  The 1-D theory of flow in the arteries yields an equation for the wave speed
in terms of the density of blood and the distensibility of the vessel. By means
of this equation there is a duality between the equation for the wave speed and
the tube law describing the area of the vessel as a function of pressure. We
explore this duality for the equations for wave speed and tube laws that are
most commonly used in theoretical arterial hemodynamics. We see that there are
qualitative differences between these laws and the experimental data on wave
speed in canine arteries measured by Anliker and his colleagues 50 years ago.
We suggest an empirical equation for wave speed (and its dual tube law) that
fits the experimental data as well as the common expectation that arteries
become stiffer as the pressure increases. We conclude with a cautionary
historical tale about the differences between the theoretical predictions and
the experimental measurements of the speed of sound in air that persisted for
more than 200 years.
