Idealized models of reed woodwinds. Part I: Analogy with the bowed string

Elementary models of the bowed string and of woodwinds are reviewed in order to underline their analogy. The comparison of the pressure-flow characteristics of a woodwind with the friction characteristics of a bowed string shows that the mouth pressure and the bow velocity on the one hand, and a static flow parameter for the embouchure and the static force applied by the instrumentalist perpendicularly to the motion of the string on the other hand are analogous parameters. Using idealized resonators, conical resonators are found to be analogous to a string bowed elsewhere than at the middle, the position of the bow being analogous to the length of the truncation of the conical tube. A consequence of these analogies is that idealized woodwinds can be modeled with two reflection functions like a bowed string, and that some references dealing with the bowed string can be useful to study reed woodwinds. The behaviour of common solutions, including the Helmholtz motion, is finally detailed within the scope of Raman's model applied to woodwinds.