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The prediction of reverberant sound fields generated by a directional source is of great interest because practical sound sources are not omnidirectional, especially at high frequencies. For an arbitrary directional source described by cylindrical and spherical harmonics, this paper developed a modal expansion method for calculating the reverberant sound field generated by such a source in both two-dimensional and three-dimensional rectangular enclosures with finite impedance walls. The key is to express the modal source density using the cylindrical or spherical harmonic expansion coefficients of the directional source. A method based on the fast Fourier transform is proposed to enable the fast computation of the summation of enclosure modes when walls are lightly damped or rigid. This makes it possible to obtain accurate reverberant sound fields even in a large room and/or at high frequencies with a relatively low computational load. Numerical results with several typical directional sources are presented. The efficiency and the accuracy of the proposed method are validated by the comparison to the results obtained using the finite element method. [ABSTRACT FROM AUTHOR]

In this work, a cylindrical expansion for the audio sound generated by a steerable baffled parametric array loudspeaker (PAL) based on the phased array technique is derived from the Westervelt equation. The expansion is a series of twofold summations with uncoupled angular and radial components in the cylindrical coordinate system. The angular component is determined by the trigonometric functions, and the radial component is an integral containing the Bessel functions and an arbitrary excitation velocity profile. The numerical results for a typical steerable PAL are presented and compared to those obtained using the convolution model. It is found that the prediction of the audio sound using the proposed cylindrical expansion improves the agreement with the experimental results when compared to the existing models. This is because no further approximations are required in the cylindrical expansion of the quasilinear solution of the Westervelt equation, whereas the complex near field nonlinear interactions between the ultrasonic waves cannot be correctly captured in a convolution model. The proposed cylindrical expansion does, therefore, provide an alternative approach to modeling a phased array PAL and high accuracy with a relatively low computational cost. [ABSTRACT FROM AUTHOR]