Longitudinal Scattering in Strings

A waveguide section between two partial sections

a)

Physical picture indicating traveling waves in a continuous medium with wave impedance changing from $R_0$ to $R_1$ to $R_2$ along the horizontal axis, resulting in signal scattering (power-conserving transmission and reflection)

b)

Digital simulation diagram

Such a rod might be constructed, for example, using three different materials having three different densities