The p-p intensity probe consists of two microphones, closely matched in phase. By exploiting the spatial distance between the microphones, we can find the pressure gradient of the sound field. This pressure gradient is related to the particle velocity

where u_x is the particle velocity, ∆r is the distance between the microphones, ρ is the air mass density and p₁, p₂ is the sound pressure of microphone 1 and 2, respectivly.

From the equation, we may see that an increased spacer distance will make the particle velocity less sensitive to the difference between the pressure of mic 1 and 2. This is an important property, as the microphones in the real world are not perfectly phase-matched. This is also the relatity for the input stages in the intensity analyser.

As mentioned above, when the sound field is active only, the sound intensity is directly related to the sound pressure. In the opposite case, a diffuse field, we will have high sound pressure but no intensity.

On a sound intensity analyser, the degree of reactivity may be determined from the ratio between Sound pressure and sound intensity. In dB values, we use the field indicator F_pI for this: F_pI = L_p - L_I. A high F_pI means high reactivity, while F_pI = 0 means a completely active sound field. A negative F_pI value is physically impossible, and would normally indicate turbulent air around the probe or a bad phase mismatch.

The upper frequency is limited by the error introduced by the spacer distance. When the wavelength becomes comparable to the spacer distance, the mean sound pressure calculated from mic 1 and mic 2 will introduce errors because of the amplitude difference. When half the wavelength distance corresponds to the spacer distance, it is no longer possible to calculate the direction of the sound field unambigously any more.

The error of the sound intensity is present for all frequencies, altough negligible for low frequencies. The upper frequency limit is defined in IEC 61043 as when the error is larger than 1 dB. The error is calculated from following formula

The error is plotted for different frequencies below:

The limitation frequencies obtained from this formula may be seen here:

Selecting spacer

The lower frequency limitation is limited by the phase mismatch between the microphones, preamplifiers and input channels in the analyser. When ∆r becomes small, it is difficult to determine the difference and the phase mismatch becomes significant compared to the pressure gradient.

In terms of intensity measurements, a phase mismatch will produce bad intensity levels. The result may be that the indicated intensity is higher or lower than the real intensity. Especially for highly reactive fields, the mismatch causes problems.

The IEC 61043 standard specifies a quantity to determine the phase mismatch of the measurement system. This is the pressure-residual intensity index δ_pI0 [dB], which is defined as the F_pI when the probe microphones are exposed to an identical pink noise sound field.

In the ISO 9614 standard for sound power measurements, the limitation is quantified using a Dynamic Capability Index (L_d = (δ_pI0 - K) [dB]). Here, K is a margin constant of either 10 or 7 dB, depending on the accuracy. The requirement is that the F_pI is not above L_d.

In the Nor145, the L_d may be significantly improved by performing a calibration on a compatible probe. Please see the links below for further information about phase calibration.

Intensity theory

Measurement surface theory

Phase calibration theory

Probe calibration

The Nor1290 probe

The Nor1294 coupler

Sound Intensity help index