One-Dimensional Acoustic Models of Horns and Comparison with Measurements

Due to the simple properties of plane waves, non lossy straight pipes and their concatenation have been extensively used to derive digital waveguide synthesis and to compute acoustic immittances (input impedance, transmittance, etc) of wind instruments. This paper focuses on some possible refinements of such 1D wave propagation models, especially in the case of smooth horns. Four key points are examined: a refined curvilinear 1D horn equation, the smooth connection of constant-flared acoustic pipes, a radiation model consistent with spherical wavefronts, the effect of visco-thermal losses at the wall. They allow the definition of a complete model, from which a standard matrix formalism is recovered, as for plane or spherical waves. The comparison with measurements shows that each of these refinements is relevant, making one-dimensional models useful and efficient even for the quite sensitive case of brass instruments. Moreover, compared to the standard descriptions based on straight or conical pipes, the model proposed here gives accurate descriptions with only a few segments.