Frequency Domain Estimation of the Complex Acoustic Intensity and Acoustic Energy Density.

This study investigates the frequency domain estimation of the active and reactive acoustic intensity and the potential and kinetic energy densities. The frequency domain representation for these acoustic field quantities are derived for stationary ergodic processes. It is shown that these estimators require only the measurement of the auto- and cross-spectral densities between closely spaced pressure sensors. The bias and random error for these estimators are investigated. A general frequency domain representation for estimator bias is given for both instrumentation magnitude and phase mismatch and the finite-sum and finite-difference approximations for the acoustic pressure and particle velocity. It is shown that the active intensity bias due to instrumentation channel phase mismatch is directly related to the ratio of potential energy to the active acoustic intensity. The reactive intensity is shown to be sensitive to the magnitude mismatch between the measurement channels. The experimental instrumentation developed to measure the vector acoustic intensity and scalar energy density is described. Measurement results are presented for a variety of acoustic sources in different acoustic environments. The effect of acoustic field reverberation is experimentally investigated. It is shown that the active intensity estimator can ignore standing wave energy. It is also shown that the reactive intensity is useful in locating acoustic sources in highly reverberant environments and identifying standing wave directions. A computer model is developed that allows the calculation of the complex acoustic intensity and the energy densities for an arbitrary spatial arrangement of amplitude and phase shaded point sources. This model is used to compare some of the measured results with predicted results and the agreement is very good. The vector differential properties for the active and reactive intensity vector fields are investigated. The results show that the active intensity vector field is in general rotational, and in a source free region; solenoidal. The reactive intensity vector field is found to be irrotational and non-solenoidal. The scalar potential field for the reactive intensity is shown to be proportional to the potential energy scalar field.