This book highlights the mathematical and physical properties of acoustical sources with singularities located in the complex plane and presents the application of such special elements to solve acoustical radiation and scattering problems. 

Sources whose origin lies in the complex plane are also solutions of the wave equation but possess different radiating properties as their counterparts with real positions. Such mathematical constructions are known in the fields of optics and electrodynamics, but they are not common in acoustical research. The objective of the book is to introduce this concept to acousticians and motivate them to engage themselves in further research and application of complex sources. Such sources are particularly useful to formulate Green’s functions and related equivalent source and boundary element methods in half-spaces.

This book highlights the mathematical, physical, and technical properties of moving acoustic sources. Authors consider point sources and infinite or finite line sources moving along various curves in three-dimensional space. After studying the general theory of such sources, the frequency spectrum and the associated Doppler shift are derived explicitly for different trajectories. The sound radiation in half-spaces with a locally reacting and homogeneous ground is investigated in detail based on the knowledge of closed-form solutions for the stationary impulse response. An important field of application is the localization of moving sources. Among other approaches, an equivalent source method in the time domain is used to develop an effective source localisation method. Important practical applications are explored with these techniques, e.g. the detection of noise sources from trains and airplanes.

The research results published in this book are mainly obtained within the three-year project “Localization and identification of moving noise sources” funded by the German Research Foundation.

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This book highlights the mathematical and physical properties of acoustical sources with singularities located in the complex plane and presents the application of such special elements to solve acoustical radiation and scattering problems. 

Sources whose origin lies in the complex plane are also solutions of the wave equation but possess different radiating properties as their counterparts with real positions. Such mathematical constructions are known in the fields of optics and electrodynamics, but they are not common in acoustical research. The objective of the book is to introduce this concept to acousticians and motivate them to engage themselves in further research and application of complex sources. Such sources are particularly useful to formulate Green’s functions and related equivalent source and boundary element methods in half-spaces.

This book highlights the mathematical, physical, and technical properties of moving acoustic sources. Authors consider point sources and infinite or finite line sources moving along various curves in three-dimensional space. After studying the general theory of such sources, the frequency spectrum and the associated Doppler shift are derived explicitly for different trajectories. The sound radiation in half-spaces with a locally reacting and homogeneous ground is investigated in detail based on the knowledge of closed-form solutions for the stationary impulse response. An important field of application is the localization of moving sources. Among other approaches, an equivalent source method in the time domain is used to develop an effective source localisation method. Important practical applications are explored with these techniques, e.g. the detection of noise sources from trains and airplanes.

The research results published in this book are mainly obtained within the three-year project “Localization and identification of moving noise sources” funded by the German Research Foundation.

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