Boundary Conditions

$\begin{figure}\centerline{\scalebox{1}{% \input{2medium.pstex_t}}} \end{figure}$

The pressure and velocity at the junction must be equal (continuity--they are shared by both mediums).
The pressure at the junction is given by

$\displaystyle p(J) = p_i(J) + p_r(J),$

$\displaystyle p_i(J)$ $\displaystyle \triangleq$ the indicident wave at the junction

$\displaystyle p_r(J)$ $\displaystyle \triangleq$ the reflected wave at the junction $\displaystyle .$
The incident and reflected pressure waves correspond to incident and reflected airflow by

$\displaystyle p_i(J) = Z_1U_i(J)$
and

$\displaystyle \qquad p_r(J) = -Z_1U_r(J),$
- the negative sign accounts for the fact that airflow is a directional quantity and moves in the direction in which it generates pressure.

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

$\displaystyle p_i(J)$	$\displaystyle \triangleq$	the indicident wave at the junction
$\displaystyle p_r(J)$	$\displaystyle \triangleq$	the reflected wave at the junction $\displaystyle .$