Use of the complex intensity vector for sound radiation and sound field studies

Abstract

The traditional intensity technique to determine the sound power radiated by sources or propagating through a sound field uses the real part of the complex intensity only. More information on the sound field and sound radiation can be obtained if both real and imaginary components of the intensity vector are considered. This paper presents the results of studies of the fundamental relationships between sound pressure, particle velocity, complex intensity, and both potential and kinetic energy. As shown before, the real part of the intensity vector is rotational (curl Ir ≠ 0, div Ir ≠ 0), while the imaginary (reactive) component of the complex intensity vector is irrotational (curl Ii = 0, div Ii ≠ 0). The conditions of the vortex formation were studied as a function of the source distribution. The relation between the extremes of the intensity curl and the energy in the sound field have been formulated. The applications of the sound intensity field structure on the sound radiation from complex radiators is shown using specific examples. New graphical methods of presenting the intensity field are shown. The paper also presents experimental results obtained by an automatic computer controlled system for intensity measurements.