3-D sound intensity measurements: Accuracy enhancements with virtual-instrument-based technology

This paper describes a method that allows accuracy and bandwidth enhancements in 3-D sound intensity measurements. Commercial 3-D probes are usually set up with three mutually perpendicular 1-D p-p probes and, thus, arranged with six microphones; although sound intensity can be calculated with 15 independent pairs of transducers, only the three primary pairs that are aligned with the coordinate system axes. The other 12 secondary pairs consist of mutually perpendicular microphones, which are placed at a distance that is v root 2 times shorter than the primary one. The main idea of the proposed method is to average the intensity that is measured on primary and secondary pairs. This leads to a larger bandwidth, thanks to the shorter separating distance between secondary pairs. The intrinsic r-p method high-frequency sensitivity loss is partially recovered, starting from the theoretical plane wave expression. Measurements of different axes are weighted with coefficients that are computed by optimizing the measurement uncertainty. Errors that are due to the metrological characteristics of the transducers and the effects of environmental conditions are compensated. Experimental results showed that a p-p probe arranged with half-inch microphones that are placed at a distance of 50 mm allows reliable measurements up to 2.5 kHz, whereas a commercial probe bandwidth with the same configuration is usually 1250 Hz.