The radiating part of circular sources - Mathematical PhysicsReport as inadecuate

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Abstract: An analysis is developed linking the form of the sound field from a circularsource to the radial structure of the source, without recourse to far-field orother approximations. It is found that the information radiated into the fieldis limited, with the limit fixed by the wavenumber of source multiplied by thesource radius Helmholtz number. The acoustic field is found in terms of theelementary fields generated by a set of line sources whose form is given byChebyshev polynomials of the second kind, and whose amplitude is found to begiven by weighted integrals of the radial source term. The analysis isdeveloped for tonal sources, such as rotors, and, for Helmholtz number lessthan two, for random disk sources. In this case, the analysis yields thecross-spectrum between two points in the acoustic field. The analysis isapplied to the problems of tonal radiation, random source radiation as a modelproblem for jet noise, and to noise cancellation, as in active control of noisefrom rotors. It is found that the approach gives an accurate model for theradiation problem and explicitly identifies those parts of a source whichradiate.

Author: Michael Carley


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