Two Impedance Steps

Physical stress and velocity at far left of section $i$:

$$\begin{eqnarray*} f_i &=& f^{{+}}_i+ f^{{-}}_i \\ v_i &=& v^{+}_i+ v^{-}_i\nonumber \end{eqnarray*}$$

• Let $x_i \in[0, cT]$ denote axial position in section $i$
• $f_i(t,x_i) \mathrel{\stackrel{\mathrm{\Delta}}{=}}f^{{+}}_i(t-x_i/c)+f^{{-}}_i(t+x_i/c)$ is the stress at position $x_i$ and time $t$ within section $i$