Calculating reflection coefficient (velocity)

Likewise, the new impedance may be given in terms of velocity components

$\displaystyle Z_2 = \frac{p(J)}{U(J)} = Z_1\frac{U_i(J)-U_r(J)}{U_i(J)+U_r(J)}$

The reflection coefficient is calculated as:

$\displaystyle Z_1\frac{U_i - U_r}{U_i + U_r}$	$\displaystyle =$	$\displaystyle Z_2$
$\displaystyle Z_1(U_i - U_r)$	$\displaystyle =$	$\displaystyle Z_2(U_i + U_r)$
$\displaystyle U_i(Z_1 - Z_2)$	$\displaystyle =$	$\displaystyle U_r(Z_1+Z_2)$
$\displaystyle \frac{U_r}{U_i}$	$\displaystyle =$	$\displaystyle \frac{Z_1-Z_2}{Z_1+Z_2}.$

``Music 206: Digital Waveguides'' by Tamara Smyth, Department of Music, University of California, San Diego (UCSD).