Error analysis of a practical energy density sensor

The investigation of an active control system based on acoustic energy density has led to the analysis and development of an inexpensive three-axes energy density sensor. The energy density sensor comprises six electret microphones mounted on the surface of a 0.025-m (1 in.) radius sphere. The bias errors for the potential, kinetic, and total energy density as well as the magnitude of intensity of a spherical sensor are compared to a sensor comprising six microphones suspended in space. Analytical, computer-modeled, and experimental data are presented for both sensor configurations in the case of traveling and standing wave fields, for an arbitrary incidence angle. It is shown that the energy density measurement is the most nearly accurate measurement of the four for the conditions presented. Experimentally, it is found that the spherical energy density sensor is within +/- 1.75 dB compared to reference measurements in the 110-400 Hz frequency range in a reverberant enclosure. The diffraction effects from the hard sphere enable the sensor to be made more compact by a factor of 3 compared to the sensor with suspended microphones.