Source‐resonator modeling: a rough paradox

Abstract

Using the example of a short pipe loaded by a free reed located upwards, we will underline the fact that a reflection function based modeling will not give the same results (and synthesized sounds) as an unsteady incompressible and lossless Bernoulli description while this model is commonly assumed to be a low‐frequency limit case of the first one, and that the second description is the only valid one. This paradox will be explained and it will be underlined why the so‐called electro‐acoustical analogies do not constitute a low‐frequency limit case of reflection function or input impedance descriptions, based on a waves paradigm. Extension to striking reeds and/or longer pipes, as found in saxophone, clarinet or sheng for instance, will be discussed and a strange coupling between a priori incompatible models, commonly used in Musical Acoustics notably, will be described.