Nonlinear Acoustics in Brass Instruments

Abstract eng:
Since the work of Stokes in 1848 it has been well known that sound propagating over large distances begins to distort due to the accumulation of small nonlinear effects. It can be shown that plane sound waves in a straight duct will eventually steepen to form discontinuous shocks (in the absence of viscosity). More recently experiments have shown that this distortion and the resulting shock waves may be responsible for the characteristic “brassy” sound of trombones and trumpets - especially when played at louder volumes [1]. The mathematics however, describing this nonlinear behaviour in ducts with curvature - such as the trombone resonator - remains little understood. Our work extends the Multimodal Method of F´elix and Pagneux [2] [3] with the introduction of a ‘nonlinear admittance’ term coupling pressure and velocity modes to give a description of nonlinear behaviour in ducts with curvature.

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