Physical realization of the radiation of complex multipoles
* Presenting author
Complex multipoles are sound sources located at positions having an imaginary component. They are also solutions of the Helmholtz equation, but their radiation patterns are different from those of their real counterparts. If rq is the complex source position, the source preferably emits the sound in a direction indicated by Im(rq) and the degree of focusing depends on the amplitude of Im(rq). A loudspeaker in a box behaves at low frequencies like a monopole, a loudspeaker without a box like a dipole and a tuning fork like a longitudinal quadrupole. In contrast, complex multipoles do not have simple physical equivalents, since they are pure mathematical constructions. In the present work, the sound radiation of complex multipoles will be modelled by an array of loudspeakers whose amplitudes are determined so, that their radiation pattern is reproduced. To obtain the amplitude of each loudspeaker, a combination of the Boundary Element Method (BEM) and the Equivalent Source Method (ESM) is applied. With the BEM the transfer function of each loudspeaker is calculated and with the ESM their amplitude by minimizing the error at certain control points.