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Recently, energy quadratization and modal expansion have become popular methods for developing efficient physics-based sound synthesis algorithms. These methods have been primarily used to derive explicit schemes modeling the collision between a string and a fixed barrier. In this paper, these techniques are applied to a similar problem: modeling a distributed mouthpiece lay-reed-lip interaction in a woodwind instrument. The proposed model aims to provide a more accurate representation of how a musician’s embouchure affects the reed’s dynamics. The mouthpiece and lip are modeled as distributed static and dynamic viscoelastic barriers, respectively. The reed is modeled using an approximate modal expansion derived via the Rayleigh-Ritz method. The reed system is then acoustically coupled to a measured input impedance response of a saxophone. Numerical experiments are presented.

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