Volume Velocity at Junction

Volume velocity at the junction is the sum of the incident and reflected velocity waves:

$$U(J) = U_i(J) + U_r(J).$$

Incorporating the result for the incident pressure wave:

$$p_i(J) = Z_1U_i(J),$$

and reflected pressure wave:

$$\qquad p_r(J) = -Z_1U_r(J),$$

volume velocity at the junction is

$$U(J)= \frac{1}{Z_1}(p_i(J)-p_r(J)).$$