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TitleCylindrical harmonic expansion of the sound field due to a rotating line source
Publication TypeConference Paper
Year of Publication2010
AuthorsPoletti, M.A.
Conference Name20th International Congress on Acoustics 2010, ICA 2010 - Incorporating Proceedings of the 2010 Annual Conference of the Australian Acoustical Society
Date Published2010
KeywordsAcoustic field measurement, Acoustic fields, Acoustic generators, Acoustic sources, Aeroacoustics, Amplitude and frequency modulations, Circular wavefronts, Direction of motion, Doppler shifting, Expansion, Fixed frames, Fixed points, Harmonic expansion, Line sources, Linear motion, Linear wave equation, Loudspeaker system, Loudspeakers, Mach cone, Point sources, Radiated sound, Rotation speed, Rotational speed, Sound source, Source frequency, Source position, Source speed, Surround sound
AbstractThe motion of an acoustic source relative to some fixed frame produces a Doppler shifting of the source frequency at a fixed point relative to that frame. For linear motion of the source greater than the speed of sound, the radiated sound forms a shock wave whose angle relative to the direction of motion varies with source speed. Some applications in acoustics involve a sound source rotating around a fixed point in space. For example, in surround sound systems, it may be desirable to generate the sound due to a sound source which moves around the listener. As another example, the Leslie speaker is a rotating loudspeaker system designed to produce amplitude and frequency modulation effects. In aeroacoustics, the noise produced by rotating propellers or rotors is of interest and the linear wave equation solution for a rotating source has some relevance. The description of rotating sources also has applicability in other disciplines such as electromagnetism and astronomy. This paper develops a cylindrical harmonic expansion for the sound field produced by a rotating line source. The expansion has a simple form and reverts to the standard expression for a fixed line source when the rotation speed is zero. For rotational speeds where the source is supersonic, the sound field produced by the expansion produces features similar to those demonstrated for rotating supersonic point sources, such as a Mach cone emanating from the source position, a spiral cylinder within which the field produces a spiralling pattern, and an inner cusp where the circular wavefronts converge. The expansion is implemented in matlab using a truncated form of the expansion, and examples of sound fields are given for both subsonic and supersonic cases. Copyright © (2010) by the International Congress on Acoustics.

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