A model that accurately computes the sound pressure field of a loudspeaker would be an efficient tool for designing a real transducer system. Although there are many tools for calculating radiation and diffraction from loudspeaker cabinets, the results are only valid for high frequencies; traditional approaches for modeling diffraction produce significant errors at frequencies below 500 Hz. This research describes an approach to solve the 3-dimensional Helmholtz equations of a piston radiator in a rectangular solid enclosure using the Method of Fundamental Solutions. This method enables accurate calculation of sound pressure, including an exact representation of diffraction. The radiation impedance of a piston in a finite enclosure can also be computed. In practice, there is a maximum frequency that depends on the cabinet size. The low- and high-frequency models can then be smoothly joined.
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