A series expansion in ascending powers of the wavenumber k is derived for the acoustic power delivered by baffled or unbaffled planar sources. This series provides a relatively simple means of deriving expressions for the power radiated by a baffled source with a known velocity distribution and can be used for unbaffled plates when the velocity field outside the plate is also known. The terms in the series are calculated from the moments of this velocity distribution in the plane containing the source. If these moments are written as derivatives in wavenumber space, it is shown that a MacLaurin expansion of the Fourier transformed velocity provides an easy technique for computing the first few terms of the acoustic power. Examples are provided for baffled, rectangular plates with various boundary conditions. The arbitrarily shaped plate with free boundaries is particularly interesting. It is proven that the volume flow across its surface must be zero and as a result corner and edge mode radiation cannot exist for this kind of source.

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