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Simplified Impedance Analysis

The above results are quickly derived from the general reflection-coefficient for force waves (or voltage waves, pressure waves, etc.):

$\displaystyle \zbox {\rho = \frac{R_2-R_1}{R_2+R_1} = \frac{\mbox{Impedance Step}}{\mbox{Impedance Sum}}} \protect$ (5.22)

where $ \rho$ is the reflection coefficient of impedance $ R_2$ as ``seen'' from impedance $ R_1$. In other words, if a wave $ f^{{+}}$ traveling along in impedance $ R_1$ suddenly hits a new impedance $ R_2$, the wave will split into a reflected wave $ f^{{-}}=\rho f^{{+}}$, and a transmitted wave $ (1+\rho)f^{{+}}$. It therefore follows that a velocity wave $ v^{+}$ will split into a reflected wave $ v^{-}= - \rho v^{+}$ and transmitted wave