To measure sound intensity accurately using a two-microphone technique, you need a reliable sound intensity probe set containing a matched microphone pair to obtain information on both the instantaneous pressure and pressure gradient in the sound field. The microphones are separated by a fixed distance in the sound field, and the microphone signals are fed to a sound intensity processor which calculates the sound intensity. The sound intensity is calculated from the time average of the sound pressure multiplied by the particle velocity (calculated from the measured pressure gradient). Such a system measures the component of the sound intensity along the probe axis and also indicates the direction of energy flow.
Sound Intensity Probe Set 3595 is intended for use with 2260 Investigator. The Dual Preamplifier Type 2683 with Microphone Pair Type 4197, Extension Stem UA 1439 and Handle with Integral Cable UA 1440 can also be used with other intensity systems, e.g., NEXUS™ Conditioning Amplifier Type 2691. The characteristics of the Sound Intensity Probe Kit Type 3595 and Sound Intensity Microphone Pair 4197 are described in the Product Data sheet.
The sound intensity probe is constructed on a face-to-face design. It consists of a robust frame which holds the microphone preamplifier(s) and matched microphones in a face-to-face configuration. The distance between the microphones is defined by solid plastic spacers which are held in place by threaded studs on the microphone grids. Sound is constrained to act on each microphone through a narrow slit between the spacer and the microphone grid. This arrangement gives well-defined acoustic separation of the microphones and minimises shadow and reflection effects.
The probe is strong but lightweight and can be held using either a handle with integral cable ending in a 10 pin LEMO plug or with an extension rod. The probe can be connected to 2260 Investigator via a cable or an extension rod. All the probe sets are supplied in transport cases containing a microphone pair, windscreen (ellipsoidal) and accessories.
The case has pockets to accomodate 2260 Investigator, a Sound Level Calibrator Type 4231 and other small accessories.
Type 3595 is supplied with 1/2" Sound Intensity Microphone Pair Type 4197. These microphones operate on a polarization voltage of 200 V.
Sound intensity microphone pairs
Phase matching of the 1/2" microphone pair Type 4197 is better than 0.05° between 20 Hz and 250 Hz, and is better than f/5000 degrees at higher frequencies, where f is the frequency. Such phase matching is possible as a result of the integral microphone phase-corrector units (patented) which are fitted to the 4197 microphones. The normalised microphone frequency responses differ by less than 0.2 dB up to 1 kHz and by less than 0.4 dB up to 7.1 kHz.
Type 4197 is supplied with 8.5 mm, 12 mm and 50 mm spacers. Calibration data provided include phase matching up to a 1/3-octave centre frequency of 6.3 kHz, microphone sensitivities at 250 Hz, actuator responses and individual free-field frequency responses valid for the microphones mounted on a 1/4" preamplifier.
Brüel & Kjær also supplies a 1/4" Microphone Pair Type 4178 which consists of a pair of 1/4" microphones, phase matched to better than 0.2° from 20 Hz to 1 kHz and sensitivity matched to better than 1 dB. Type 4178 is supplied with 6 mm and 12 mm spacers, along with calibration charts giving the individually measured free-field frequency response for each microphone.
IEC 1043 standard
The IEC 1043 standard (Electroacoustics – Instruments for the measurement of intensity – measurement with pairs of pressure sensing microphones, 1993) distinguishes between Probe, Processor and Instrument and classifies them according to the measurement accuracy achieved. There are two degrees of accuracy, Class 1 and Class 2. The Brüel & Kjær probe set complies with IEC 1043 Class 1 which has the most stringent tolerance requirements. Note, however, that the IEC standard only specifies the frequency range from centre frequencies of 50 Hz to 6.3 kHz in 1/3-octave bands.
The useful free-field frequency range according to IEC 1043 Class I for Type 3595 using the various microphone and spacer combinations, is from 1/3-octave centre frequencies of 50 Hz to 6.3 kHz. However, using the actuator response correction described in an article by Prof. F. Jacobsen in Brüel & Kjær’s Technical Review Nr. 1, 1996 (BV 0048), the frequency response can be extended to 10 kHz using just the 12 mm spacer. The actual frequency range in practice depends on the difference between the pressure and intensity levels, i.e., Pressure-Intensity Index, which is dependent on the nature of the sound field and the phase response deviation between the probe and processor channels.
The frequency range depends on the difference between the pressure level and the intensity level. In most field measurements, the sound intensity level is lower than the sound pressure level. The ability of a sound intensity instrument to measure intensity levels much lower than the pressure level depends on the probe and processor phase matching. The difference between pressure and intensity levels is called the Pressure-Intensity Index which is denoted by dpI and is normally a positive quantity.
dpI0 is the Pressure-Residual Intensity Index of the measurement instrumentation (shown for the probe by the limits of the shaded area in Fig. 5). dpI0 is determined by the phase (mis)match of the system, and its effect on the accuracy of a measured sound intensity level is determined by the value chosen for the constant K. If K is 7 dB, then an accuracy of ± 1 dB can be expected. If K is 10 dB then the accuracy will be ± 0.5 dB (the sign of this bias error depends on the sign of the system’s phase mismatch). Measurements must be restricted to values of dpI given by:
dpI£dpI0 – K
The Pressure-Residual Intensity Indices for the intensity probe set, shown in Fig. 5 (solid lines), are derived directly from the phase matching specifications.
As the static pressure equalization vent may cause problems, the IEC 1043 standard specifies that probes designed to operate at frequencies below 400 Hz must be tested in a plane standing wave field. The standing wave ratio must be 24 dB at a frequency between 125 and 400 Hz. Fig. 6 illustrates the performance of the Brüel & Kjær intensity probe for this test at 125 Hz.
The upper limit of the frequency range for a sound intensity probe set depends on the length of the microphone spacer. Approximating the pressure gradient using two microphones separated by a short distance in the sound field leads to an underestimate of the sound intensity level, butthe error is less than 1 dB as long as the distance between the microphones is less than one sixth of the wavelength. This means that for high-frequency measurements, a short spacer should be used. The bias error is plotted as a function of frequency for the different microphone spacers in Fig. 7. To keep this error to less than 1 dB, the appropriate spacer is chosen for the frequency range of interest. 50 mm, 12 mm and 8.5 mm spacers are used with 1/2" microphones up to 1/3-octave centre frequencies of 1.25 kHz, 5 kHz and 6.3 kHz respectively; 12 mm and 6 mm spacers with 1/4" microphones up to 1/3-octave centre frequencies of 5 kHz and 10 kHz respectively.
Extension of frequency range to 10 kHz using 1/2" microphones and 12 mm spacer is described in Brüel & Kjær Technical Review No.1 1996 and Product Data sheet for 2260.
Effective acoustical separation of probe microphones
It is important that a sound intensity probe does not disturb the sound field it is measuring. The face-to-face configuration and the optimised mechanical design of the Brüel & Kjær probe means that the disturbance of the sound field is very small.
The spacers used to separate the microphone pairs in the sound field are designed to give acoustic separations of 6 mm, 8.5 mm, 12 mm and 50 mm. Their physical lengths in fact differ slightly from these values. The effective acoustical separation of the microphones varies slightly as a function of frequency due to reflections. This effect is minimised by the solid spacers which separate the microphones, and the distance variation is less than 0.5 mm for the 12 mm spacer. The effect on the accuracy of the measured sound intensity is consequently very small.
The typical response shown in this graph includes all the possible sources of error: phase mismatch, free-field corrections, microphone distance variation and the high-frequency approximation error (the latter giving a - 1 dB error at centre frequencies of 1.25 kHz, 5 kHz and 6.3 kHz respectively).
Patented microphone phase-corrector units
The phase matching specified for the 4197 microphone pair is retained even in sound fields with very high pressure-level gradients, such as those found close to point sources. This is a benefit of the patented phase-corrector units which are fitted to these microphones. Ordinary condenser microphones can have their phase responses altered if there is a difference between the pressure level at the pressure equalisation vent and that at the diaphragm. Type 4197 microphones are, however, essentially insensitive to sound at the vent and the accuracy of near-field measurements at low frequencies is consequently increased .
Phase calibration of the 1/2" Microphone Pair Type 4197 is done at Brüel & Kjær by subjecting the two microphones to the same sound signal in a pressure coupler. This individual phase calibration can be used to derive the actual Pressure-Residual Intensity Index for the microphone pair. If only amplitude (pressure) calibration is required, the two channels can be calibrated separately using a Pistonphone Type 4228 or together using Sound Level Calibrator Type 4231 with Coupler DP 0888.