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Optimal shape of the reflex tube of a bass loudspeaker

 
: Mohring, J.; Jegorovs, J.; Klein, D.

Sas, P. ; Katholieke Universiteit Leuven, Departement Werktuigkunde:
Noise and vibration engineering. Proceedings of ISMA 2004. CD-ROM : Leuven, 2004 September 20 - 22; International Conference on Noise and Vibration Engineering
Leuven: Katholieke Universiteit Leuven, 2004
ISBN: 90-73802-82-2
ISBN: 978-90-73802-82-7
pp.3877-3890
International Conference on Noise and Vibration Engineering (ISMA) <2004, Leuven>
English
Conference Paper
Fraunhofer ITWM ()

Abstract
If a strong sinusoidal signal is sent to a vented bass loudspeaker we do not only hear the fundamental frequency, but also higher harmonics not present in the original signal. This nonlinear distortion is partially due to the response of the electro-mechanical components and partially due to the transfer behavior of the enclosed air. Here, we investigate the latter effect. In particular, we show how to design a reflex tube in order to reduce the induced first overtone to a minimum. Obviously, the problem cannot be formulated in the framework of linear acoustics. On the other hand, solving the full Euler equations in each step of a shape optimization is impracticable. Therefore, we propose a correction to the linear Helmholtz equation. In contrast to the classical second order equation of nonlinear acoustics it consists just in a second inhomogeneous Helmholtz equation for the first harmonic and an algebraic equation for the radiation pressure. The system of linear PDEs may be solved sequentially. A Lagrangian description takes into account moving boundaries in a natural way and pressure is chosen as unknown rather than the velocity potential, which cannot be measured.

: http://publica.fraunhofer.de/documents/N-172494.html