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A model problem for a reactive silencer is solved by calculating the scattering of acoustic waves at sharp edges in a two-dimensional waveguide. An exact analytical solution is found using the Wiener-Hopf technique. Control methods are developed and employed to check the theory and the accuracy of the numerical results.

Negative real parts of impedances can be found in IC-engine source characterization measurements. There is an obvious problem with the physical interpretation of negative resistances, and consequently there have been many questions about the validity of such results. This paper is an attempt to explain the origin of the mentioned negative acoustic resistances. To this end, a simple nonlinear lumped acoustic system, that is, a force-driven damped mass-spring system, is analyzed. Since this is a common case in acoustic measurements, linear analysis is performed in spite of the obvious nonlinear properties. It is shown that the degree of nonlinearity in the system is crucial to the values of the acoustic impedance. Furthermore, it is shown that it is possible to achieve negative resistances already in a simple lumped system. Finally, these results are also compared to simulated and measured IC-engine source impedances.