Scattering at Impedance Changes

When a traveling wave encounters a change in wave impedance, scattering occurs, i.e., a traveling wave impinging on an impedance discontinuity will partially reflect and partially transmit at the junction in such a way that energy is conserved. This is a classical topic in transmission line theory [296], and it is well covered for acoustic tubes in a variety of references [298,367]. However, for completeness, we derive the basic scattering relations below for plane waves in air, and for longitudinal stress waves in rods.