Vecherin S. N., D. K. Wilsom and V. Ostashev (December 2011): Incorporating source directionality into outdoor sound propagation calculations. J. Acoust. Soc. Am., 130, 3608-3622. doi:10.1121/1.3655881Full text not available from this repository.
Many outdoor sound sources, such as aircraft or ground vehicles, exhibit directional radiation patterns. However, long-range sound propagation algorithms are usually formulated for omnidirectional point sources. This paper describes two methods for incorporating directional sources into long-range sound propagation algorithms. The first is the equivalent source method (ESM), which determines a compact distribution of omnidirectional point sources reproducing a given directivity pattern in the far field. This method can be used with any propagation algorithm because it explicitly reconstructs a source function as a set of point sources with certain amplitudes and positions. The second is a directional starter method (DSM), which is developed specifically for the parabolic equation (PE) algorithms. This method derives narrow- or wide-angle directional starter fields, corresponding to a given source directivity pattern, without reconstructing the equivalent source distribution. Although the ESM can also be used for the PE, the DSM is simpler and can be more convenient, especially if the sound propagation is calculated only for one or a few azimuthal directions. While these two methods are found to produce generally distinct starter fields, they nonetheless yield identical directivity patterns.
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