Loudspeaker behaviour under incident sound fields

Abstract

Within the framework of an outdoor active noise control project, a need arose, namely to establish whether electrodynamic loudspeakers are likely to be affected by the primary noise or by the interactions between them. The aim of this thesis is therefore to provide computation and measurement methods allowing to predict whether the effects of an incident sound field on a loudspeaker have to be taken into account. The study comprises two main parts involving modelling, theory and calculations for the first part, and experimental validations in an anechoic chamber for the second one. The equivalent circuit modelling of an electrodynamic loudspeaker shows that its behaviour can be completely determined from its input impedance. The thesis starts with the reflection that the modifications in loudspeaker behaviour due to the presence of an incident sound pressure applied on its radiating membrane could then also be analysed in the same way. The chosen process then consists in analysing the loudspeaker modifications in behaviour, no longer as variations of its radiation impedance, but as variations of its volume velocity and input impedance. The latter, which is located at the electrical loudspeaker terminals, offers the advantage of being easily measurable. Within the scope of this thesis, the loudspeakers are assumed to behave like flat rigid pistons. Based on Thiele and Small parameters and using Rayleigh's surface integral and the unified and geometrical theories of diffraction, the calculations enable input impedance, volume velocity, near and far field sound pressure, as well as medium reaction force and radiation impedance to be obtained for each loudspeaker. Taking into account interaction effects, they also enable the modifications of all these quantities in modulus and phase to be predicted. A discrete approach is chosen in order to minimize the computation time. The calculations were however fine tuned in such a way as to ensure sufficient accuracy in relation to measurement uncertainties. In order to evaluate the orders of magnitude of the modifications in loudspeaker behaviour, some preliminary calculations are first carried out in the simple case of two closed-box loudspeakers mounted in the same infinite baffle. This part also leads to understand how input impedance and volume velocity modifications vary according to excitation ratio, excitation difference of phase and distance between piston centres. Then and in order to get closer to realistic configurations, the calculations are carried out in the cases of two adjacent and distant closed-box loudspeakers. A test bench enables then the effects of an incident sound field on a closed-box loudspeaker to be measured. The configuration is chosen in order to eliminate any diffraction and significant mutual effects likely to distort the results. The aim of this first experiment is to highlight every potential measurement difficulty in order to determine the measurement setup, as well as to validate the choice of the measured quantities (input impedance and volume velocity). Once the orders of magnitude of the modifications in loudspeaker behaviour are evaluated, the study focuses on three different loudspeaker configurations beginning with the most simple case of two closed-box systems mounted in a baffle, and ending with most realistic ones, corresponding to the configurations of loudspeakers mounted in an array (two adjacent and distant closed-box systems). It is worth noting here that the measurement accuracy of the Thiele and Small's parameters plays an essential role in this study. The results of the measurements carried out in each configuration are finally compared to the theoretical predictions, enabling calculation methods to be validated.