The radiation efficiency grouping of free-space acoustic radiation modes

The use of a modal representation for the exterior acoustic field of a stru cture has received increasing attention in recent years. This modal approac h generally seeks a set of orthogonal functions, representing independent s urface velocity distributions, termed acoustic radiation modes, which diago nalize a radiation operator in the exterior domain of the structure. These orthogonal acoustic radiation modes may be found, among other methods, thro ugh an eigenvalue analysis of a radiation operator and possess a correspond ing set of eigenvalues that are proportional to the radiation efficiencies of the acoustic radiation modes. In free space, the acoustic radiation mode s of a sphere display a grouping characteristic in their radiation efficien cies, where each acoustic radiation mode's radiation efficiency within a gr oup has the same frequency dependency. This is a consequence of the fact th at the acoustic radiation modes of a sphere al-e the spherical harmonics. F urther, the acoustic radiation modes of an arbitrary three-dimensional stru cture exhibit the same frequency grouping as those for the sphere. The basi s for the arbitrary structure's grouping follows from the sphere's grouping . The observation that the acoustic radiation modes of an arbitrary body ar e dominated by spherical harmonics provides insight on the behavior of such modes. These results have significance for various applications of acousti c radiation modes, including active noise control design, radiation modelin g, etc. (C) 2001 Acoustical Society of America. [DOI: 10.1121/1.1323236].