Updated: Oct 9
Acoustic intensity spectra presented in linear or 1/3 octave frequency bands are useful in understanding the vector sound field, in addition to scalar pressure measurements commonly available using microphones. Unfortunately, due to their cost and need for precise calibration, triaxial intensity measurements have not been widely used in noise monitoring work, nor have noise monitoring standards adopted acoustic vector sensor measurements.
Intensity can be expressed as:
I = p u* / 2
where p is the scalar pressure, u is a measure of the triaxial particle velocity, and u* indicates the complex conjugate of u. Measuring the 3-d intensity vector of a sound field as a function of frequency facilitates discrimination of noise sources by direction (azimuth and elevation angles), in addition to frequency and relative amplitude.
Until now, two methods have been used to estimate acoustic intensity. Both employ microphones to measure pressure but differ in how particle velocity is estimated. One way is to observe the difference in pressure between two closely spaced microphones, which is referred to as the p-p method of calculating sound intensity. A finite difference approximation, in which particle velocity is approximated by a differential in the pressure between microphones, is combined with the average pressure across both microphones to compute intensity. The microphone separation distance can restrict application of the p-p method to frequencies sufficiently low such that the wavelength exceeds this distance by a factor of five or more. Triaxial p-p probes are configured by spatially distributing microphones in three dimensions, ideally with a concentric reference point, with the microphones carefully phase matched by selection or calibration to avoid low frequency measurement errors.
A second particle velocity estimation method differentially measures the change in resistance of two closely spaced thin wires in a sound field. When sound propagates across the wires, it asymmetrically alters the temperature distribution around the resistors, which after calibration is proportional to acoustic particle velocity. Three pairs of electrically stimulated wires, along with a microphone to measure acoustic pressure is generally referred to as a triaxial p-u sound intensity probe. When accurately calibrated, it can measure particle velocity over a wide frequency range . Both p-u and p-p probes arrive at the particle velocity estimate indirectly via estimation of an indirect physical process (heat advection and pressure differentials, respectively).
ARES technology is a new third method that employs a triaxial accelerometer to measure acoustic particle velocity [1, 2] via integration. In contrast to the p-u or p-p approaches, the p-a method directly measures the triaxial inertial velocity of a fixed volume of air. This volume is extended beyond the physical dimension of the accelerometer by placing the device within a very lightweight solid sphere which has density as close to air as possible. This solid volume encloses both the microphone and accelerometer, so this method offers improved shielding from environmental effects over both p-u and p-p systems. An accelerometer based acoustic vector sensor provides excellent noise source directional resolution by directly computing Equation 1, using 4-channel time synchronized measurements of pressure, and (integrated) acceleration on each of three orthogonal axes. MEMS accelerometers are DC-coupled, i.e., can sense low frequencies without phase error, and thus offer an improvement to finite difference techniques implemented using phase matched p-p intensity probes. Sensitivity to the Earth’s gravitational field provides a convenient and accurate calibration method.
The following table summarizes the three intensity measurement methods and describes their respective limitations in frequency range.
 Dall’Osto, D., et al. Airborne vector sensor experiments within an anechoic chamber, J. Acoust. Soc. Am. 144, 1854 (2018).
 Dall’Osto, D., & Dahl, P. Preliminary estimates of acoustic intensity vorticity associated with a turbine blade rate, J. Acoust. Soc. Am. 142, 2701 (2017).
 de Bree, H., An overview of microflown technologies, Acustica, Volume 89, Number 1, January/February 2003, pp. 163-172