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Second Order Correction of Acoustic Helmholtz Equation
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Tags: acousticsasymptotic_analysishelmholtzhelmholtz_equationnon_linear_acoustics
Added by Martin on 20110712 15:52
Second Order Correction of Acoustic Helmholtz Equation If a strong sinusoidal signal is sent to a vented bass loudspeaker we will hear not only the fundamental frequency, but also higher harmonics. This nonlinear distortion is partially due to the response of the electromechanical components and partially due to the transfer behavior of the enclosed air. Here, we deal with the latter effect. It is well known that the edges of reflex tubes have to be chamfered to avoid noise. The present model is designed to investigate this phenomenon with minimal numerical costs . Obviously, linear acoustics are insufficient. Solving the full Euler equations, however, requires an unreasonably high effort. Therefore, we propose a correction to the linear Helmholtz equation which consists just in a second inhomogeneous Helmholtz equation for the first harmonic and an algebraic equation for the radiation pressure. For medium displacements it allows to predict how the energy inserted into the loudspeaker at a given frequency is distributed between the keynote and the first harmonic.