Ohm's Law for Traveling Waves

We just derived Ohm's Law for Traveling Waves on an Ideal String

where the velocity waves are defined in terms of transverse string displacement by

$$\begin{eqnarray*} v^{+}(n) &\mathrel{\stackrel{\mathrm{\Delta}}{=}}& \dot y^{+}(n)\\ v^{-}(n) &\mathrel{\stackrel{\mathrm{\Delta}}{=}}& \dot y^{-}(n), \end{eqnarray*}$$

$f^{{+}}$ and $f^{{-}}$ are corresponding force waves, and $R\mathrel{\stackrel{\mathrm{\Delta}}{=}}\sqrt{K\epsilon }$ is the wave impedance of the string:

$$\zbox{R \;\mathrel{\stackrel{\mathrm{\Delta}}{=}}\;\sqrt{K\epsilon } \;=\;\frac{K}{c} \;=\;\epsilon c}$$