Block diagram of a played trombone in its environment. First, the pipe is described by a quadripole. The two inputs are the mouthpiece volumetric flow rate, denoted U_in and the pressure at the bell, denoted P. The two outputs are the flow rate at the bell, U_tb and the mouthpiece pressure P_in. Second, the radiation is represented by a linear impedance load Z_R (equal to P/U_tb in the Laplace domain). And the transfer impedance T_R(r) between U_tb and the pressure P_out(r) at a point r. Note that in all the paper, flow rates are algebraic quantities counted positively in the direction of e_ℓ (e.g., U_in=U_ine_ℓ).