A refined physical model of the clarinet using a variable air jet height

A time-domain formulation of a lumped model approximation of a clarinet reed excitation mechanism is presented. The lumped model is based on an analytical representation of the flow within the reed channel, incorporating a contraction coefficient (vena contracta factor) that is defined as the ratio of the effective flow over the Bernoulli flow. This coefficient has been considered to be constant in previous studies focusing on sound synthesis. In this paper it will be treated as a function of the reed opening, varying between 0 and 1 as predicted by boundary layer flow theory. Focussing on a specific mouthpiece geometry, the effect of modelling a variable air jet height on the synthesised sound is analysed.