A multipole expansions method for acoustic wave propagation in vocal tract

The paper investigates the problem of wave motion in a vocal tract. We try to solve the problem using the Helmholtz equation, one of the most important mathematical models used to describe the time harmonic behavior of various vibration and wave propagation phenomena. The motivation of our work is to understand the main characteristics of wave propagation in the vocal tract, which is modeled as a series of 8 concatenated tubes. Some examples of research applications include human speech production, speech recognition and speaker identification. Some of the characteristic quantities to be calculated in these problems include scattering amplitudes, transmission and reflection coefficients, and resonance frequencies. We use multipole expansions to derive a closed form solution of the problem. For testing the method, we show the numerical results for the case of a disc where the solution is well known. Our approach shows excellent results. We intend to extend the method for the three dimensional case and to related inverse problems.