information:filtering
Measurement

where I ^ n p − u {\displaystyle {\hat {I}}_{n}^{p-u}} is the biased estimate obtained using a p-u probe, P {\displaystyle P} and V n {\displaystyle V_{n}} are the Fourier transform of sound pressure and particle velocity, J n {\displaystyle J_{n}} is the reactive intensity and φ ue {\displaystyle \varphi _{\text{ue}}} is the p-u phase mismatch introduced by calibration errors. Therefore, the phase calibration is critical when measurements are carried out under near field conditions, but not so relevant if the measurements are performed out in the far field. The “reactivity” (the ratio of the reactive to the active intensity) indicates whether this source of error is of concern or not. Compared to pressure-based probes, p-u intensity probes are unaffected by the pressure-to-intensity index, enabling the estimation of propagating acoustic energy in unfavorable testing environments provided that the distance to the sound source is sufficient.