Stage M2 – Asymptotic numerical approximations of tailored Green’s functions for acoustic predictions – Application to sound scattering by a flutist’s head
In playing conditions, a musician and its instrument are in close interaction. Thus, a complete analysis of musical instruments must include the effects of the musician’s body on the instrument mechanical behavior. For instance, insome flute-like instruments, the pitch of the sound emitted by the instrument is dependant on the flutist’s face position with respect to an open-end of the pipe, from where acoustic waves originate. An important feature of an instrumentis its directivity, which is likely to be affected by the musician’s body by scattering. The propagation of acoustic waves in the absence of surfaces is easily described by the free-space Green’s function G0. When solid surfaces are present in the propagation medium, it is possible to find a Green’s function with vanishing normal derivative ∂G/∂n= 0. Such a function is said to be tailored to the geometry and allows fast estimations of the acoustic field in the presence of surfaces with arbitrary shape. Cases where the tailored Green’s function is known analytically are however restricted to very elementary geometries. The main objective of this internship is to determine asymptotic approximations of tailored Green’s functions for shapes of arbitrary complexity in the long-wave length (orlow-wavenumber) limit.
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