The power radiated by a vibrating body in an acoustic fluid and its determination from boundary measurements

The power radiated into a specified angular sector by a vibrating object immersed in a fluid is expressed as a quadratic functional of the boundary normal velocity field. The diagonalization of the functional, obtained through the singular value decomposition of its discretized version, identifies a set of orthonormal boundary velocity patterns, each corresponding to a far-field pattern belonging to a set of functions orthonormal in the angular sector of interest. Any boundary normal velocity field can be represented as a linear superposition of the orthonormal patterns. The velocity patterns having high radiation efficiencies form a subset, whose dimension depends upon the object boundary shape and size in wavelengths. The other velocity patterns do not radiate efficiently and contribute mainly to the evanescent field in the neighborhood of the object. Assuming that some noise is present, only the radiation patterns associated with the efficiently radiating velocity patterns are observable in the far field. Therefore, the dimension of their set defines the number of degrees of freedom of the far field. The efficiently radiating velocity patterns constitute a set of spatial filtering functions, separating the radiating from the essentially nonradiating components of an arbitrary boundary normal velocity field.