Performance Analysis of Cost-Effective Miniature

sensors

Article Performance Analysis of Cost-Eﬀective Miniature Microphone Sound Intensity 2D Probe

Witold Mickiewicz 1,*, Michał Raczy ´nski 1 and Arkadiusz Parus 2

1 Faculty of Electrical Engineering, West Pomeranian University of Technology, 70-310 Szczecin, Poland; [email protected] 2 Faculty of Mechanical Engineering and Mechatronics, West Pomeranian University of Technology, 70-310 Szczecin, Poland; [email protected] * Correspondence: [email protected]

Received: 10 December 2019; Accepted: 30 December 2019; Published: 3 January 2020

Abstract: This article presents the functional properties of modified versions of the 2D pressure–pressure intensity probe allowing us to determine the vector of sound intensity on a plane using a mechatronic system with one or two miniature electret microphones. The introduction contains basic information about the application areas of the sound intensity and its measurement problems. Next, the principle of operation of the probes and the construction of the prototype measurement system are described. It was subjected to comparative analysis for the stability of obtained results and accuracy of directional characteristics in free field conditions. For this purpose, experiments were conducted to analyze the flow of acoustic power in an anechoic chamber using both (one- and two-microphone) probes. The results were used for a comparative metrological analysis of the described methods and to indicate the advantages and disadvantages of both constructions. The next part of the article presents an experiment concerning the measurement of the sound intensity impulse response of a room, which is an example of practical use of the probe to analyze reflections in the room, which can be used in sound engineering and architectural acoustics.

Keywords: sound intensity; intensity probe; pp-probe; sound source localization

1. Introduction Localization of acoustic energy sources and visualization of the vector distribution of the acoustic field around them have, on the one hand, cognitive applications and, on the other hand, many practical applications. The most important applications are: localization of noise sources, measurement of acoustic power in the presence of interference [1], support for voice communication systems, spatial sound engineering in audiovisual systems [2], acoustic localization of threats in security systems, and many others [3]. For this reason, it is important to develop commonly available acoustic sensors that enable the above-mentioned functionalities to be realized. The basic element of a spatial perception system is the presence of a sensory system containing at least two pressure sensors at some distance from each other. In the case of human beings, thanks to their two ears, they are able to locate sound sources based on the recording of pressure signals characterized by an interaural time difference and an interaural intensity difference, variable in the function of the angle of attack of a sound wave. This bionic approach to the spatial location of sound sources is widely used to produce spatial sound recordings (various types of two- and multi-microphone systems) [4,5]. Today, we also know more advanced solutions using microphone arrays and digital signal processing algorithms for spatial filtering—beamforming or acoustic holography [6]. However, these methods require an increasing number of pressure transducers and multi-channel acoustic signal acquisition

Sensors 2020, 20, 271; doi:10.3390/s20010271 www.mdpi.com/journal/sensors Sensors 2020, 20, 271 2 of 15 and processing systems and also the large size and complexity of the support constructions. For this reason, the use of such techniques is difficult or impractical in many fields. An alternative to beamforming (which is mainly based on signal processing of sound pressure) are methods based on the use of vector quantities describing the acoustic field, i.e., the acoustic particle velocity and intensity. The sound intensity measurement technique was developed in the 1930s, but the first successful measurements of this quantity date back to 1970 [7]. The first measurement devices were launched in 1980 and 10 years later the first standard describing the method of measuring the sound intensity was published. In this method, the acoustic particle velocity component is determined by determining the acoustic pressure gradient by synchronous measurement at two points in space and allows the acoustic particle velocity component to be determined in one plane [8,9]. A sensor of this type is a pressure probe type p–p (pressure–pressure). In order to determine the spatial distribution of the sound intensity, it is necessary to use three pairs of mutually perpendicular microphones (there are also known solutions using only four microphones for this purpose). Unlike sound pressure measurements (scalar quantity), sound intensity measurements are not trivial. It requires specialized equipment and precision of electroacoustic transducers [10,11]. These facts influence the high price of these types of solutions. There are also limitations of determining the sound intensity over a wide frequency range, related to the physical size of the intensity probe. With the development of miniaturization, there has been a breakthrough in the measurement of acoustic particle velocity and sound intensity. At the beginning of the 21st century, new sensors were introduced to the market, based on a different principle, known as Microflown [12]. It is a p–u-type sensor (pressure–velocity), which means that the component of the acoustic particle velocity is determined using a different physical phenomenon than the occurrence of the acoustic pressure gradient. It is an anemometric sensor with hot wires. In this sensor, the movement of acoustic particles causes heat to flow between areas around two conductors placed close to each other and creates a temperature difference between them. A change in temperature causes a change in resistance that can be measured with an electronic system [13]. This sensor has introduced a new quality of sound intensity measurement, mainly due to its small dimensions and the ability to determine sound intensity over a wide frequency range. Unfortunately, this sensor also has disadvantages. Due to the principle of operation, its failure-free operation time is relatively short (about two to three years of intensive use) in relation to the high price. There is also a recurring interest in the above-mentioned method of measuring sound intensity using the p–p probe. A major difference to previous solutions based on the use of expensive, precisely adjusted pairs of microphones is the use of miniature electret microphones (commonly used in audiological equipment) or MEMS (microelectromechanical system) microphones widely used in mobile phones. Exact microphone selection is now replaced by procedures for the correction of amplitude and phase-frequency characteristics. The correction is based on real parameters of used microphones obtained from direct measurement. A final conformity of transducers (removing the discrepancies between them) is obtained by digital filtering. This approach is presented, for example, in the works [14–16]. Like any measurement method, despite its many advantages, it also has some disadvantages. The main problem is, first of all, the need for preliminary calibration and estimation of correction coefficients. The proposed procedures require the use of anechoic chambers and specialized equipment. Furthermore, due to the long-term change in the parameters of individual microphones in the probe, it is expected that the necessary calibration process must be repeated periodically to be sure of the metrological parameters of the probe. In the opinion of the authors, an important aspect that influences a stagnation in the wider use of intensity methods is the cost of equipment, especially professional intensity probes. The aim of the research presented in this paper is an objective evaluation of the metrological quality of modified intensity probes based on the principle of operation of p–p probes, made with the use of fewer inexpensive transducers and a mechatronic positioning system. Sensors 2020, 20, 271 3 of 15

2. Principle of Operation of the Intensity Probe An acoustic ﬁeld is most often described by two physical quantities: sound pressure and acoustic particle velocity. Another quantity, sound intensity, is the function of these two quantities. Due to the simplicity of the measurement procedure, the sound pressure pa is most often measured, which is a scalar indicating the instantaneous change in pressure around a constant value (in the case of air, it is usually the atmospheric pressure): pa = p(t) p (1) − 0 where p0 is the atmospheric pressure, p(t) is the instantaneous value of pressure, and t is a time. Equation (1) describes the instantaneous value of the sound pressure, which can be both positive and negative and varying around the constant value of atmospheric pressure. The meters used in acoustical measurements always determine the positive Root Mean Square (RMS) of the sound pressure according to the formula: uv tu Zt 1 t τ p (t) = p2(τ )e −T dτ (2) aRMS T a − −∞ where T-value is the detector’s time constant (in sound level meters, values of 125 ms (FAST mode) and 1 s (SLOW mode) are most frequently used) and τ is the independent variable (time). The scale of RMS values heard by a human ear is very wide: 2 10 5 Pa to 200 Pa. For this reason, × − it is comfortable to use decibel measurement and to determine the sound pressure level (SPL): paRMS SPL = 20 log (3) 2 10 5Pa · − Thus, deﬁned scalar quantities measured in a single point of space do not carry any information about the direction (sense and orientation) of acoustic energy propagation. The propagation of the acoustic wave causes local movement of the medium in which the wave propagates. It is the movement of the acoustic particles. An acoustic particle is a correspondingly small volume of a medium of a size much smaller than the wavelength. At the same time, it contains so many molecules of the medium that it can be assigned the whole volume averaged thermodynamic parameters (e.g., pressure). Acoustic particles can be assigned an acoustic particle velocity. In contrast to acoustic pressure, it is a vector and has three components in the Cartesian coordinate system:

→ → → →u(t) = i ux + j uy + k uz (4) where i, j, and k are unity vectors of coordinate system. Using the deﬁnition of acoustic particle velocity, it is possible to introduce the concept of sound intensity (vector quantity), which describes the ﬂow of acoustic energy in a medium. The instantaneous value of the sound intensity Iinst(t) can be expressed as the product of the sound pressure pa(t) and the velocity of the sound particle →u(t):

−−→I (t) = pa(t) →u(t) (5) inst · The mean value of the instantaneous sound intensity is called the active component of the sound intensity and is determined as follows: Z 1 T −→Iact = −−→Iinst(t)dt (6) T 0

W The unit of sound intensity is m2 . The instantaneous sound intensity is a vector quantity with its orientation consistent with the vector of acoustic particle velocity. The magnitude and direction of this vector, however, depends on the sound pressure value. Since, as mentioned earlier, the instantaneous sound pressure values can Sensors 2020, 20, 271 4 of 15 be positive or negative, the intensity vector direction can be the same as the velocity vector or the opposite. This means that the sound intensity is influenced by the phase relation between the pressure wave system and the acoustic particle velocity wave system. In the free far-field, where the observed waves can be considered as flat, the phase shift between the pressure wave and the velocity wave is zero, the direction of the sound intensity vector coincides with the propagation direction, and the direction indicates the energy flow from the source to the surrounding space. The observation of the intensity of sound thus gives a more accurate view of the phenomena in the acoustic field, taking into account the interactions of many sources (real and apparent) and their individual amplitude-phase characteristics. Hence, the authors’ interest are in the problem of intensity measurements and their use in sound engineering (especially in the auralization of recordings) and architectural acoustics—the relationship between acoustic properties of rooms and time–space analysis of intensity impulse responses of rooms. Nowadays, two types of intensity probes are the most common: the p–u probe and the p–p probe. In the p–u probe, pressure and acoustic particle velocity are measured with the use of different types of sensors. A microphone is used to measure the pressure and an ultrasonic (Norsonic, Tranby, Norway) or hot-wire anemometric transducer (Microflown, Arnhem, The Netherlands) is used to measure the acoustic particle velocity. In the p–p probe, the acoustic particle velocity is determined indirectly from the pressure gradient measured by a pair of microphones placed in close distance to each other according to the Euler’s linearized equation: Z 1 ∂p(t) →u(t) = dt (7) −ρ ∂→x where u—acoustic particle velocity; ρ—density of environment; p—acoustic pressure; x—space variable. After discretization, Equation (7) takes the following form:

Z t 1 pa1(τ) pa2(τ) →u(t) = − dτ (8) −ρ ∆x −∞ The gradient of acoustic pressure is substituted by the finite difference of two acoustic measurements done by a pair of microphones, which should be identical. The lower integration limit is the beginning of the test signal. To measure one, two, or three components of the sound intensity vector accordingly one, two, or three pairs of microphones are necessary, placed orthogonally to each other. The upper measurement frequency range is limited by the proper approximation of a derivative by finite difference. The low frequency range is limited by phase mismatch error and noise of the measured signal. The typical distance is 12 mm and provides measurements in the frequency range: 125 Hz–5 kHz. A general disadvantage of p–p probes is the necessity to use microphones that have identical amplitude and phase-frequency characteristics. In practice, it is impossible to obtain perfect matching. Thus the complex calibration procedures and/or correction of characteristics by analog or digital filters are necessary.

3. Modification of the Pressure–Pressure Method In the case of measurement of acoustic systems whose parameters can be assumed to be constant during the measurement procedure and where the measurement can be performed repeatedly by emitting identical excitation signals, the design of a standard p–p probe can be modified. Firstly, all the components of the intensity vector can be measured using a two-microphone probe type p–p, positioning only one pair of microphones accordingly. Further on, each component can be determined based on a sequence of measurements with one microphone in successive positions corresponding to the distribution of microphones in classical p–p 1D, 2D, or 3D probes. Such an approach was already mentioned many years ago [7,8], but only nowadays it is practically feasible thanks to the development of computer measurement systems guaranteeing proper synchronization of the generation of the Sensors 2020, 20, 271 5 of 15 excitation signal and data acquisition and accurate and repeatable methods of positioning. Not without significance is also the development of miniature microphone transducers with a wide bandwidth, flat frequency response, and low noise. These facts prompted the authors to undertake the presented research. Some achievements in this field have already been presented in [15,17,18]. Sensors 2020, 20, x FOR PEER REVIEW 5 of 16 4. 2D Mechatronic Sound Intensity Probe Construction 4. 2D Mechatronic Sound Intensity Probe Construction The measurements described in the next chapters were carried out with the use of the author’s The measurements described in the next chapters were carried out with the use of the author’s own construction of the 2D probe. Although the probe has two microphones, it can also be used as own construction of the 2D probe. Although the probe has two microphones, it can also be used as a a single-microphone probe. In this case, one microphone is switched off. Construction details are single-microphone probe. In this case, one microphone is switched off. Construction details are shown in Figure1a,b. The probe consists of a base to which a stepper motor is attached. The motor shown in Figure 1a,b. The probe consists of a base to which a stepper motor is attached. The motor shaft is connected to the bearing metal rod on which the plastic header with pair a of microphones is shaft is connected to the bearing metal rod on which the plastic header with pair a of microphones is placed. Two cylindrical miniature electret microphones with a diameter of 1/10 inch (Sonion 8011 [19]) placed. Two cylindrical miniature electret microphones with a diameter of 1/10 inch (Sonion 8011 [19]) are placed in the header rolled out of ABS plastic. Details of the header are shown in Figure2. are placed in the header rolled out of ABS plastic. Details of the header are shown in Figure 2. The The distance between the microphone axes is 10 mm. The microphones’ fronts are placed on the surface distance between the microphone axes is 10 mm. The microphones’ fronts are placed on the surface of the probe header. By placing the microphones perpendicular to the sound intensity measurement of the probe header. By placing the microphones perpendicular to the sound intensity measurement plane, the amplitude-phase characteristics are guaranteed to remain unchanged, especially in the high plane, the amplitude-phase characteristics are guaranteed to remain unchanged, especially in the frequencies, as a function of the angular position of the microphone in relation to the sound source. high frequencies, as a function of the angular position of the microphone in relation to the sound The electronic part of the probe includes low-noise microphone preamplifiers with a battery power source. The electronic part of the probe includes low-noise microphone preamplifiers with a battery supply and a stepper motor controller with mains power supply. The whole measurement is performed power supply and a stepper motor controller with mains power supply. The whole measurement is by a dedicated LabVIEW virtual device responsible for the generation and acquisition of measurement performed by a dedicated LabVIEW virtual device responsible for the generation and acquisition of signals and the generation of control sequences for the stepper motor. Probe positioning is carried out measurement signals and the generation of control sequences for the stepper motor. Probe digitally in an open feedback loop. positioning is carried out digitally in an open feedback loop.

Figure 1. Construction of the 2D sound intensity probe based on two microphones (dimensional units Figure 1. Construction of the 2D sound intensity probe based on two microphones (dimensional units are millimeters); (a) photo of real probe; (b) construction details. are millimeters); (a) photo of real probe; (b) construction details.

Figure 2. Construction details of the header of the mechatronic 2D sound intensity probe based on two microphones.

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4. 2D Mechatronic Sound Intensity Probe Construction The measurements described in the next chapters were carried out with the use of the author’s own construction of the 2D probe. Although the probe has two microphones, it can also be used as a single-microphone probe. In this case, one microphone is switched off. Construction details are shown in Figure 1a,b. The probe consists of a base to which a stepper motor is attached. The motor shaft is connected to the bearing metal rod on which the plastic header with pair a of microphones is placed. Two cylindrical miniature electret microphones with a diameter of 1/10 inch (Sonion 8011 [19]) are placed in the header rolled out of ABS plastic. Details of the header are shown in Figure 2. The distance between the microphone axes is 10 mm. The microphones’ fronts are placed on the surface of the probe header. By placing the microphones perpendicular to the sound intensity measurement plane, the amplitude-phase characteristics are guaranteed to remain unchanged, especially in the high frequencies, as a function of the angular position of the microphone in relation to the sound source. The electronic part of the probe includes low-noise microphone preamplifiers with a battery power supply and a stepper motor controller with mains power supply. The whole measurement is performed by a dedicated LabVIEW virtual device responsible for the generation and acquisition of measurement signals and the generation of control sequences for the stepper motor. Probe positioning is carried out digitally in an open feedback loop.

SensorsFigure2020, 20 1., Construction 271 of the 2D sound intensity probe based on two microphones (dimensional units6 of 15 are millimeters); (a) photo of real probe; (b) construction details.

Figure 2. Construction details of the header of the mechatronic 2D sound intensity probe based on SensorsFigure 2020, 20 2., xConstruction FOR PEER REVIEW details of the header of the mechatronic 2D sound intensity probe based on6 of 16 two microphones. two microphones. 5. Measurement of the Flow of Acoustic Energy in an Anechoic Chamber 5. Measurement of the Flow of Acoustic Energy in an Anechoic Chamber In order to compare the metrological quality of the proposed measurement methods, two experimentsIn order were to compare carried out the at metrological the West Pomeranian quality of University the proposed of Technology measurement in Szczecin, methods, Poland two experimentsin the hemi-anechoic were carried chamber out at with the Westa working Pomeranian space of University 2 m (length) of Technology × 2.5 m (height) in Szczecin, × 1.5 m Poland (width). in theIt can hemi-anechoic be assumed (it chamber is a consequence with a working of the hemi space-anechoic of 2 m (length) chamber dimensions)2.5 m (height) that the1.5 mconditions (width). × × Itof canthe befree assumed field are (it maintained is a consequence for frequencies of the hemi-anechoic above 300 Hz. chamber dimensions) that the conditions of theThe free sound ﬁeld are source maintained was the for frequenciesGenelec 8040 above [20] 300 two-way Hz. active loudspeaker system. The measurementThe sound probe source was was located the Genelec 1 m from 8040 the [20 front] two-way of the active loudspeaker. loudspeaker The system.location The of the measurement measuring probestation was elements located is 1 mshown from thein Figure front of 3. the The loudspeaker. application The controlling location of the the measurement measuring station process elements was islaunched shown on in Figurean industrial3. The computer application PXie-1082 controlling equipped the measurement with acquisition process and generation was launched cards on type: an industrialPXIe-6368 and computer PXIe-4499 PXie-1082 [21]. The equipped resolution with of the acquisition analog-to-digital and generation converter cards used type: is 24 bits, PXIe-6368 while andthe digital-to-analog PXIe-4499 [21]. Theconverter resolution is 16 bits. of the The analog-to-digital data sampling frequency converter in used all experiments is 24 bits, while was 100 the digital-to-analogkHz. The system converterensured isthe 16 synchronization bits. The data sampling of acquisition frequency and ingeneration all experiments processes was with 100 kHz. the Theaccuracy system of ensuredthe 0.01 the sample. synchronization The sensitivity of acquisition of the andwhole generation acquisition processes path (microphone with the accuracy with ofa thepreamplifier) 0.01 sample. was The 0.361 sensitivity V/Pa for of one the microphone whole acquisition and 0.374 path V/Pa (microphone for the second. with a preampliﬁer)The conventional was 0.361axis of V /thePa forprobe one microphonelay on a straig andht 0.374line passing V/Pa for through the second. the Thecenter conventional of the microphones axis of the probemarked lay with on a straight“1” and line“2” passing(Figure through4). During the all center measurements, of the microphones the signals marked from with both “1” microphones and “2” (Figure were4). recorded During allsimultaneously. measurements, To the determine signals fromtwo bothcomponents microphones of sound were intensity recorded vector simultaneously. using a two-microphone To determine twoprobe, components there is necessary of sound to intensity set the probe vector in using two positions a two-microphone (e.g., 0 and probe, 180 or there 90 and is necessary 270). In case to set when the probethe one-microphone in two positions method (e.g., 0 andis used, 180 or four 90 andpositions 270).In of case probe when arethe necessary one-microphone to set. Of method course, isin used, this foursituation positions only ofone probe microphone are necessary is active. to set. Of course, in this situation only one microphone is active.

Figure 3. Cont.

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SensorsSensors 2020 2020, 20, 20, x, xFOR FOR PEER PEER REVIEW REVIEW 77 of of 16 16

Figure 3. Experimental measuring workplace. FigureFigure 3. 3.Experimental Experimental measuring measuring workplace. workplace.

Figure 4. Positioning of the head with reference to the sound source. Figure 4. Positioning of the head with reference to the sound source. Figure 4. The aim of the first experimentPositioning was of theto estimate head with the reference statistical to error the sound of measuring source. the component of soundThe aim intensity of the first using experiment the single-microphone was to estimate method the statistical in comparison error of measuringto the two the microphones component The aim of the first experiment was to estimate the statistical error of measuring the component of ofmethod sound usingintensity miniature using theelectret single-microphone microphones. In method this experiment, in comparison the axis to theof the two probe microphones was set sound intensity using the single-microphone method in comparison to the two microphones method methodaccording using to theminiature axis passing electret through microphones. the geometric In this center experiment, of the loudspeaker the axis of set. the In probe this position, was set usingaccordingtones miniature of frequenciesto electretthe axis microphones.passing250, 1000, through and In 4000 the this geometricHz experiment, were emittedcenter the of axisand the of recordedloudspeaker the probe by wasmicrophonesset. setIn this according position, in the to the axistones passingmeasuring of frequencies through probe. theThe 250, geometric same 1000, measurement and center 4000 of Hzwas the we loudspeakermadere emitted after turning set.and Inrecorded the this probe position, by by microphones 180 tones⁰ (changing of frequencies in thethe 250,measuring 1000,position and of 4000probe. microphones Hz The were same 1 emittedand measurement 2). In and each recorded of wasthese made positions, by microphonesafter theturning measurement the in theprobe measuring was by repeated 180⁰ (changing probe. 100 times. The the same measurementpositionBy using of a wasmicrophones sinusoidal made aftersignal 1 and turning as 2). an In excitation, each the of probe these the by positions,number 1800 (changing of the necessary measurement the measurement position was repeated of data microphones processing 100 times. 1 and 2). InByoperations each using of a these sinusoidal was positions,reduced, signal and the as the measurementan excitation,final statistics th wase ofnumber repeatedthe obtained of necessary 100 results times. measurement show By using directly a sinusoidaldata the processingquality signal of as an excitation,operationsthe measurement thewas number reduced, system of and and necessary thenot finalthe measurementwhole statistics process of the of data measurementobtained processing results data operations show processing. directly was the reduced, quality and of the finalthe statistics measurementThe second of the obtainedexperimentsystem and results consistednot the show whole of directlyexamining process the ofth qualitymeasuremente dependence of the ofdata measurement the processing. obtained systemresultant and value not the of the sound intensity vector on the angle of the acoustic energy flows through the probe. For this whole processThe second of measurement experiment consisted data processing. of examining the dependence of the obtained resultant value ofpurpose, the sound the intensity probe head vector was on rotated the angle around of theits axisacoustic by a stepperenergy flowsmotor. through One step the was probe. equal For to this1.8 The second experiment consisted of examining the dependence of the obtained resultant value purpose,deg. During the probefull rotation head was of the rotated head, around pressure its measurement axis by a stepper from motor.both microphones One step was was equal recorded to 1.8 of the sound intensity vector on the angle of the acoustic energy flows through the probe. For this deg.for 200During positions. full rotation Figure 4of shows the head, four pressureexample positimeasurementons of the from head both with microphones microphones wasin relation recorded to purpose, the probe head was rotated around its axis by a stepper motor. One step was equal to 1.8 deg. forthe 200 direction positions. of the Figure flow 4 of shows acoustic four energy. example positions of the head with microphones in relation to Duringthe direction fullIn each rotation ofof thethese of flow thepositions, of head, acoustic the pressure energy.loudspeaker measurement system emitted from test both signals microphones in the form was of test recorded tones for 200 positions.at frequenciesIn each Figure of theseas 4before shows positions, and four a thelogarithmically example loudspeaker positions tu systemned ofsweep theemitted headsignal test with between signals microphones in20 theHz formand in 20 of relation kHztest tones[22]. to the directionatThis frequencies ofallowed the flow asus beforeto of examine acoustic and athe energy.logarithmically properties of thetuned measurement sweep signal method between as a 20 function Hz and of 20 frequency. kHz [22]. ThisInThe each allowedrecorded of these us values to positions,examine of voltage the the signalsproperties loudspeaker corresponding of the system measurement to emittedthe values method test of signalssound as a pressurefunction in the form atof eachfrequency. of point test tones at frequenciesTheof measurementrecorded as values before were of and voltagerecorded a logarithmically signals in the correspondingform of tuned an LVM sweepto theformat. values signal The of betweenmeasurement sound pressure 20 Hz data andat wereeach 20 point kHzthen [22]. processed using original scripts in the MATLAB software. Thisof allowed measurement us to examinewere recorded the properties in the form of of the an measurementLVM format. The method measurement as a function data were of frequency. then Theprocessed recorded using values original of voltage scripts signals in the MATLAB corresponding software. to the values of sound pressure at each point of measurement were recorded in the form of an LVM format. The measurement data were then processed using original scripts in the MATLAB software. Sensors 2020, 20, 271 8 of 15

6. TheSensors Results 2020, 20 of, xthe FOR PreliminaryPEER REVIEW Experiment 8 of 16

This6. The part Results of the of article the Preliminary presents theExperiment results of the experiment described in the previous paragraph. The valuesThis of sound part of intensity the article are presented,presents the which results on theof the basis experiment of measured described values ofin acousticthe previous pressures wereparagraph. determined The using values the of formulas sound intensity below: are presented, which on the basis of measured values of acoustic pressures were determined using the formulas below: p1(n) + p2(n) I(n) = u(n) 𝑝(𝑛) +𝑝(𝑛) (9) 𝐼(𝑛) = 𝑢(𝑛) 2 (9) 2 n 11 X u(𝑢n()𝑛)== 𝑝p1(𝑘)(k) −p 𝑝 2(𝑘)(k) (10) (10) ρ𝜌f𝑓sd𝑑 − k=1

where: fs—sampling frequency; d—distance between microphones; ρ—air density (1.2 kg/m3); p1, p2—3 where: fs—sampling frequency; d—distance between microphones; ρ—air density (1.2 kg/m ); p1, instantaneous values of sound pressure registered by microphones in positions 1 and 2 (Figure 4); p2—instantaneous values of sound pressure registered by microphones in positions 1 and 2 (Figure4); 𝑛—number of sample. n—number of sample. Figure 5 shows the histograms for the determined sound intensity values for both methods, and Figurethe normal5 shows distributions the histograms fitted to the for data. the determined sound intensity values for both methods, and the normal distributions ﬁtted to the data.

35 35

30 30

25 25

20 20

15 15 number of counts number of counts number 10 10

5 5

0 0 0.996 0.998 1 1.002 0.98 0.99 1 1.01 normalized magnitude[I/Imean] normalized magnitude[I/Imean]

(a) (b)

FigureFigure 5. Statistical 5. Statistical distribution distribution of of measurement measurement results as as aa measure measure of ofrepeatability repeatability of presented of presented measurement methods. (a) Two-microphone probe and (b) one-microphone probe. measurement methods. (a) Two-microphone probe and (b) one-microphone probe. In the aim of statistical analysis of the collected data, the values of the active sound intensity In the aim of statistical analysis of the collected data, the values of the active sound intensity were were calculated as the average value of the intensity of the whole measurement time (Equation (8)). calculated as the average value of the intensity of the whole measurement time (Equation (8)). Statistical parameters for the method using one and two microphones were calculated Statisticalseparately. parameters The results are for presented the method in Table using 1. one and two microphones were calculated separately. The results are presented in Table1.

Table 1. Statistical parameters for the two-microphone and one-microphone measurement methods.

95.7% Conﬁdence Interval Standard Deviation σ 3σ (In Normal Distribution) 2-mic meth 0.001 0.003 0.01 dB ± 1-mic meth 0.005 0.015 0.07 dB ±

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Figure6 shows the distribution of the intensity vectors recorded during the probe’s incremental angular position change with reference to the sound source. Column (a) shows the results for a two-microphone probe and column (b) shows the results for a single-microphone probe. The following lines present characteristic rosettes determined for subsequent octave bands in the range from 250 Hz to 8 kHz. Such imaging of the results allows to better recognize the qualitative diﬀerences between the tested methods.Sensors 2020, 20, x FOR PEER REVIEW 10 of 16

2-mics 2D probe 1-mic 2D probe

Figure 6. The distribution of the intensity vectors of the sound when the angular position of the probe Figure 6.relativeThe distributionto the sound source of the is intensity incrementally vectors changed of the for soundthe octave when bands the from angular 250 Hz position to 8 kHz. of the probe relative to the sound source is incrementally changed for the octave bands from 250 Hz to 8 kHz.

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The ideal intensity probe should record the sound pressure level and the spatial orientation of the vector independently of its setting relative to the sound source. The vectors shown in Figure6 should be constant in length and their angle should correspond to the angular position of the probe. Due to measurement errors, this is not the case. Figure7 shows the quantitative changes in the recorded sound pressure level and the deviation of the indicated angle from the nominal value for a two-microphone probe as a function of the angular position. SensorsSensors 20202020,, 2020,, xx FORFOR PEERPEER REVIEWREVIEW 1111 ofof 1616

0.5 5 0.5 5 250Hz oct. band 250 Hz 0.4 500250Hz Hz oct. band 4 500250 Hz Hz 0.4 4 1500 kHz Hz oct. oct. band band 1500 kHz Hz 1 kHz oct. band 1 kHz 0.3 2 kHz oct. band 3 2 kHz 0.3 42 kHz kHz oct. oct. band band 3 42 kHz kHz 4 kHz oct. band 4 kHz 0.2 2 0.2 2

0.1 1 0.1 1

0 0 0 0

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-0.4 [deg] difference estimation incidence of D irection -4 Sound intensity level estimation difference [dB] [dB] difference estimation level intensity Sound

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-0.2 -2 -0.2 -2

-0.3 -3 -0.3 -3 Sound intensity level estimation difference [dB] [dB] difference estimation level intensity Sound

-0.4 [deg] difference estimation incidence of D irection -4 Sound intensity level estimation difference [dB] [dB] difference estimation level intensity Sound

-0.4 [deg] difference estimation incidence of D irection -4

-0.5 -5 -0.50 50 100 150 200 250 300 350 -50 50 100 150 200 250 300 350 0 50 1002 D p 150 ro b e p o s itio 200 n [d e g ] 250 300 350 0 50 1002 D p 150 ro b e p o s itio 200 n [d e g ] 250 300 350 2 D p ro b e p o s itio n [d e g ] 2 D p ro b e p o s itio n [d e g ] ((cc)) ((dd)) Figure 8. Variations of sound intensity magnitude (a,c) and deviation of the indicated angle from the FigureFigure 8. Variations 8. Variations of of sound sound intensity intensity magnitude (a (,ca), cand) and deviation deviation of the of indicated the indicated angle from angle the from nominal value (b,d) for a single-microphone probe for subsequent angular positions of the probe. the nominalnominal value value ((bb,,dd)) forfor aa single-microphonesingle-microphone probe probe for for subseq subsequentuent angular angular positions positions of the of probe. the probe. MicrophoneMicrophone 11 ((aa,,bb);); microphonemicrophone 22 ((cc,,dd).). Microphone 1 (a,b); microphone 2 (c,d). 7. Measurement of the Room Impulse Response 7. Measurement7. Measurement of the of the Room Room Impulse Impulse Response Response To show the utility of the proposed simplified methods of sound intensity measurement, an To showTo show the the utility utility of of the the proposedproposed simplifie simpliﬁedd methods methods of sound of sound intensity intensity measurement, measurement, an experimentexperiment waswas conductedconducted toto measuremeasure thethe impulseimpulse responseresponse ofof thethe roomroom usingusing soundsound intensity.intensity. an experiment was conducted to measure the impulse response of the room using sound intensity. TheThe impulseimpulse responseresponse obtainedobtained fromfrom thethe measurmeasurementement procedureprocedure describeddescribed inin thethe internationalinternational standardstandard ISOISO 3382-13382-1 [23][23] cancan bebe usedused toto determinedetermine ththee reverberationreverberation timetime ofof aa room.room. InIn thethe casecase ofof thethe impulseimpulse responseresponse obtainedobtained usingusing thethe methodmethod describeddescribed above,above, itit isis plannedplanned toto useuse itit forfor thethe

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The impulse response obtained from the measurement procedure described in the international standard ISO 3382-1 [23] can be used to determine the reverberation time of a room. In the case of the impulse response obtained using the method described above, it is planned to use it for the spatialization of sound recordings, which is not the subject of ISO 3382-1. Therefore, not all solutions used in the measurement process must comply with it. AnSensors omnidirectional 2020, 20, x FOR PEER sound REVIEW source should be used to measure the impulse response. ISO12 of 3382-116 describesspatialization in detail of the sound parameters recordings, to bewhich satisfied is not forthe asubject sound of sourceISO 3382-1. to be Therefore, considered not omnidirectional.all solutions The mostused in common the measurement source with process parameters must comply close with to it. omnidirectional is the dodecahedron speaker. In work [An24] omnidirectional can be found sound a description source should of otherbe used sources to measure that the can impulse be used response. as alternatives ISO 3382-1 to a dodecahedrondescribes in speaker. detail the Theparameters authors to alsobe satisfied mention for thea sound popular source electrodynamic to be considered loudspeakeromnidirectional. which, althoughThe itmost does common not meet source the requirements with parameters of theclose standard to omnidirectional for omnidirectionality, is the dodecahedron gives su speaker.fficient In results in numerouswork [24] acoustic can be measurements.found a description It is especiallyof other sources important that thatcan thebe used electrodynamic as alternatives loudspeaker to a is abledodecahedron to generate speaker. many times The authors an acoustic also mention field of the identical popular parameters, electrodynamic which loudspeaker enables which, the use of although it does not meet the requirements of the standard for omnidirectionality, gives sufficient averaging and increasing the signal-to-noise ratio—SNR (as opposed to, e.g., a gun or a pierced balloon). results in numerous acoustic measurements. It is especially important that the electrodynamic This transmitter is also characterized by its low price, which is particularly important for measuring loudspeaker is able to generate many times an acoustic field of identical parameters, which enables systemsthe thatuse of are averaging to become and more increasing popular. the signal-to- In somenoise measurements, ratio—SNR (as such opposed as speech to, e.g., intelligibility a gun or a and distortion,pierced a directionalballoon). This sound transmitter source isis betteralso charac thanterized an omnidirectional by its low price, sound which source, is particularly as stated in the IEC 60268-16important international for measuring standard. systems that are to become more popular. In some measurements, such as Anotherspeech intelligibility important aspect and distortion, of measuring a directional the impulse sound response source isis the better character than an of theomnidirectional excitation signal that powerssound source, the sound as stated source. in the The IEC most 60268-16 popular international types of signals standard. are: rectangular pulses approximating Dirac delta,Another sinusoidal important signal, aspect pseudo-random of measuring the sequences,impulse response and ais swept-sinethe character techniqueof the excitation [22] signal proposed by Farinathat powers in 2000. the ISOsound 3382-1 source. specifies The most that popular the signaltypes of level signals to are: background rectangular noisepulsesshould approximating not be less Dirac delta, sinusoidal signal, pseudo-random sequences, and a swept-sine technique [22] proposed by than 45 dB. However, when measurements are made using MLS (Maximum Length Sequence) signals, Farina in 2000. ISO 3382-1 specifies that the signal level to background noise should not be less than these45 requirements dB. However, are when lower measurements because a are better made signal-to-noise using MLS (Maximum ratio can Length be achieved Sequence) by signals, averaging. The swept-sinethese requirements method are provides lower becaus a 20 dBe a better SNR improvementsignal-to-noise ratio over ca MLSn be methods.achieved by averaging. The Basedswept-sine on the method above provides analyses, a 20 adB Genelec SNR improvement 8040 speaker over set MLS was methods. used as a source of sound in the experiment.Based It was on the powered above analyses, by the signal a Genelec of an 8040 exponential speaker set sweep was tunedused as in a the source range of ofsound 20 Hz–20 in the kHz. Its durationexperiment. was It 10was s. powered Parameters by the of signal data of acquisitionan exponential devices sweep tuned remain in the range same of as 20 inHz–20 the previouskHz. experiment.Its duration Figure was9 shows 10 s. Parameters the view of of the data examined acquisition room devices and theremain location the same of the as measurement in the previous probe and loudspeakerexperiment. Figure set and 9 itsshows standard the view pressure of the exam impulseinedresponse. room and the location of the measurement probe and loudspeaker set and its standard pressure impulse response.

(a) (b)

Figure 9. Cont.

Sensors 2020, 20, 271 12 of 15 Sensors 2020, 20, x FOR PEER REVIEW 13 of 16 Sensors 2020, 20, x FOR PEER REVIEW 13 of 16 pressure im pulse response 80

pressure im pulse response 60 80

40 60

20 40

0 20

sound pressure [Pa] pressure sound -20

-40 [Pa] pressure sound -20

-60 -40

-80 -60 0 100 200 300 400 500 600 700 800 900 1000 time [ms] -80 0 100 200 300 400 500 600 700 800 900 1000 time [ms] (c) (c) FigureFigure 9. 9.ConditionsConditions for for measuring measuring and and the the pressure pressure impulse impulse response response of aof sample a sample room; room; (a) view (a) view of sampleof sampleFigure room; room;9. ( bConditions) dimensions (b) dimensions for of measuring measurement of measurement and setup; the pressure (c setup;) standard impulse (c) standard pressure response impulse pressure of a response sample impulse ofroom; response the room. (a) view of of the room.sample room; (b) dimensions of measurement setup; (c) standard pressure impulse response of the room. Figure 10a shows the first 5 ms fragment of the obtained sound intensity impulse responses of the examinedFigureFigure 10 rooma 10a shows for shows both the firstthecomponents first 5 ms 5 fragmentms of fragment the vect of the or.of obtainedtheWe obtainedcan see sound the sound direct intensity intensity sound impulse impulse impulse responses and responses first of of earlythe examinedthereflections. examined room Figure room for 10b bothfor bothshows components components the time of evolut the of vector.theion vect of Weor. the We can successive can see thesee directtheportions direct sound ofsound energy impulse impulse reaching and and first first theearly probeearly reflections. using reflections. a color Figure Figure scale 10b showsfor10b the shows thewhole time the response evolutiontime evolut. The ofion the dark of successive theblue successive color portions indicates portions ofenergy direct of energysound reaching andreaching the firstprobe reflectionthe using probea and using color finally scalea color the for scale red the wholecolo for rthe indicates response. whole responsethe The last dark reverberation. The blue dark color blue tail. indicates color indicates direct sound direct and sound first and reflectionfirst reflection and finally and the finally red color the red indicates color indicates the last reverberation the last reverberation tail. tail. Sound intensity impulse response(first 5m s) 1 Sound intensity impulse response(first"x" component 5m s) of SI 0.8 1 "y" component of SI "x" component of SI 0.6 0.8 "y" component of SI

0.4 0.6

0.2 0.4

0 0.2

-0.2 0 normalized value normalized

-0.4 -0.2 normalized value normalized

-0.6 -0.4

-0.8 -0.6

-1 -0.8 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 time [ms] -1 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 (a) time [ms] (b) Figure 10. Sound intensity impulse(a) response of a real room. Time evolution of two intensity(b) vector components (first 5 ms) (a) and color-coded time evolution of sound intensity vector representation FigureFigure 10. Sound10. Sound intensity intensity impulse impulse response response of a of real a real room. room. Time Time evolution evolution of two of two intensity intensity vector vector on a plane (whole response) (b). componentscomponents (ﬁrst (first 5 ms) 5 (ms)a) and (a) color-coded and color-coded time evolutiontime evolution of sound of sound intensity intensity vector representationvector representation on a planeon a (whole plane (whole response) response) (b). (b). This way of visualizing the impulse response of a room compared to traditional pressure responsesThis Thisallows way way of for visualizing ofa time-spatialvisualizing the impulse analysisthe impulse response of the responseof propagation a room of compared a ofroom acoustic tocompared traditional energy to in pressure traditional the room. responses Thepressure informationallowsresponses for aabout time-spatial allows the amplitude, for analysisa time-spatial direction, of the propagationanalysis and ti meof the dependencies of propagation acoustic energy of ofthe acoustic in incoming the room. energy wave The in enables information the room. the The detectionaboutinformation the of amplitude, architectural about direction,the elementsamplitude, and in time direction, the dependenciesroom and generating time ofdependencies the favorable incoming ofor wavethe unfavorable incoming enables wave thereflections. detection enables the Figureof architecturaldetection 10b shows of elementsthearchitectural impulse in response the elements room of generating thein theroom room in favorable the generating polar or diagram unfavorable favorable and in or reﬂections. the unfavorable logarithmic Figure reflections.scale. 10 b Eachshows Figurearrow the impulserepresents10b shows response athe bit impulse of of acoustic the response room energy in the of cothe polarming room diagram from in the one andpolar direction in diagram the logarithmic until and energy in the scale. from logarithmic Each another arrow scale. directionrepresentsEach starts arrow a bit to ofrepresents arrive acoustic to the energya bit probe. of coming acoustic from energy one co directionming from until one energy direction from anotheruntil energy direction from starts another to arriveAdirection directional to the starts probe. impulse to arrive response to the probe.can also be used in sound spatialization systems by distributing it over theA directionaldirection of impulse energy response delivery can to alsoelementary be used inimpulse sound spatializationresponses that systems can be by used distributing in convolutionit over processorsthe direction to ofgenerate energy signals delivery that to supplyelementary individual impulse channels responses of surroundthat can soundbe used in systems,convolution as shown processors in Figure 11. to generate signals that supply individual channels of surround sound systems, as shown in Figure 11.

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A directional impulse response can also be used in sound spatialization systems by distributing it over the direction of energy delivery to elementary impulse responses that can be used in convolution processors to generate signals that supply individual channels of surround sound systems, as shown in Figure 11. Sensors 2020, 20, x FOR PEER REVIEW 14 of 16

Figure 11. Sound intensity impulse response of a real room as source of spatial impulse responses Figure 11. Sound intensity impulse response of a real room as source of spatial impulse responses for for surround sound systems. (FL—front left; FR—front right; C—center; SL—surround left; surround sound systems. (FL—front left; FR—front right; C—center; SL—surround left; SR— SR—surround right). surround right). 8. Discussion 8. Discussion The main novelty of the proposed single-microphone method is to replace the multi-sensor simultaneousThe main novelty measurement of the proposed of pressure single-microphone gradient components method byis to a replace sequential the multi-sensor single-sensor simultaneousmeasurement. measurement The technical problemof pressure of making gradient at least components two sensors by (including a sequential measuring single-sensor channels) measurement.with identical The characteristics technical problem is replaced of making by the problemat least two of repeating sensors (includi the measurementng measuring with channels) identical withexcitation identical and characteristics identical condition is replaced of the by measured the problem object. of repeating The identity the measurement of excitation canwith be identical affected excitationby the quality and identical of the generating condition of equipment the measured and notobject. perfect The identity synchronization of excitation between can be generation affected byand the acquisition quality of the process generating in the followingequipment steps and no oft the perfect measurement synchronization procedure. between At the generation current leveland acquisitionof development process of electronicsin the following and analog-to-digital steps of the measurement and digital-to-analog procedure. converters At the current built aslevel single of developmentintegrated circuits of electronics is the so-called and an codecs:alog-to-digital this problem and digital-to-analog is mainly related converters to the stability built of as the single clock integratedsignal, which circuits cycles is the the so-called converter. codecs: The this clock problem jitter at is the mainly picosecond related levelto the seems stability to of guarantee the clock a signal,negligible which influence cycles the of thisconverter. type of The problem clock onjitte ther at described the picosecond method. level However, seems to it isguarantee difficult toa negligibleunequivocally influence answer of thethis questiontype of problem about the on stationarity the described of the method. measured However, object. Theit is elementdifficult that to unequivocallycertainly changes answer is the the position question of about the transducer, the stationarity which, of in the principle, measured is variable. object. The To minimizeelement that the certainlyeffect of thischanges fact onis the the position distribution of the of thetransducer, measured which, field, in the principle, proposed is solution variable. uses To aminimize disk with the an effectaxis of of symmetry this fact on passing the distribu throughtion the ofaxis the ofmeasured rotation field, and two the microphones—inproposed solution the uses single-microphone a disk with an axismethod, of symmetry one transducer passing is activethrough (measuring), the axis of and rotation the other and is usedtwo microphones—in to minimize differences the single- in the microphoneprobe geometry method, when one changing transducer the position is active of the(m measuringeasuring), microphone.and the other is used to minimize differencesEquivalence in the probe of results geometry can onlywhen be changi guaranteedng the position if the subsequent of the measuring steps ofmicrophone. the measurement procedureEquivalence are carried of results out under can only identical be guaranteed conditions. if What the subsequent is certainly steps not identical of the measurement in subsequent proceduremeasurements are carried are the out interference under identical signals conditions (noise) of the. What environment is certainly and not the identical measuring in subsequent equipment measurementsitself. In order are to the minimize interference the impact signals of (noise these) phenomena,of the environment it is necessary and the tomeasuring ensure a equipment sufficiently itself.high ratioIn order of the to signalminimize level the measured impact of to these the noise phenomena, level. Therefore, it is necessary in the to presented ensure a experiments,sufficiently highthe measurementsratio of the signal were level carried measured out in anto the isolated noise room level. with Therefore, a background in the presented level not exceedingexperiments, 35 dBAthe measurementsand an SPL level were of thecarried signal out measured in an isolated at about room 90 with dBA. a Thus, background the results level presented not exceeding in Figure 35 5dBA can andbe interpretedan SPL level as of a the limitation signal measured of the accuracy at about of 90 the dBA. method Thus, resulting the results from presented the natural in Figure noise 5 of can the beapparatus. interpreted The as experiments a limitation showed of the accuracy that the assumption of the method of the resulting stationary from character the natural of the noise tested of object, the apparatus.the conditions The ofexperiments measurement showed and thethat process the assumption of generation of the and stationary registration character of measurement of the tested data object,can be the fulfilled conditions with of high measurement accuracy, and and the the statistical process of error generation introduced and regi is verystration small of inmeasurement comparison datawith can other be errors fulfilled of the with presented high accuracy, methods. and the statistical error introduced is very small in comparisonWhen measuringwith other theerrors intensity of the ofpresented sound for methods. the purpose of determining the directions from which acousticWhen energy measuring reaches the the intensity sensor, the of mainsound problem for the ispurpose to determine of determining the directional the characteristicsdirections from of which acoustic energy reaches the sensor, the main problem is to determine the directional characteristics of the 3D intensity probe. The ideal probe shall have the same accuracy in determining the direction of the energy flow independently of the location of the source in relation to the probe. Due to the lack of ideal geometric symmetry of the probe and the effects of diffraction of the acoustic field on the sensor, depending on the angle of attack of the acoustic energy flow on the microphone membrane, the accuracy of determination of the direction may vary. The second experiment showed that measurement errors in determining the magnitude and direction of the sound intensity vector are functions of the angle of attack of a sound wave. Comparing images and graphs for both probes,

Sensors 2020, 20, 271 14 of 15 the 3D intensity probe. The ideal probe shall have the same accuracy in determining the direction of the energy flow independently of the location of the source in relation to the probe. Due to the lack of ideal geometric symmetry of the probe and the effects of diffraction of the acoustic field on the sensor, depending on the angle of attack of the acoustic energy flow on the microphone membrane, the accuracy of determination of the direction may vary. The second experiment showed that measurement errors in determining the magnitude and direction of the sound intensity vector are functions of the angle of attack of a sound wave. Comparing images and graphs for both probes, it can be stated that the two-microphone probe behaves differently from the single-microphone probe, although the maximum deviations are very similar and amount to 0.3 dB and 4 deg. It is worth noting that although the ± ± two-microphone probe gives less noisy results, its errors for different frequency bands have different cycles of repetition. The errors of a single-microphone probe change cyclically every 90 degrees at all frequencies. This is important from the point of view of the correct reproduction of the amplitude of the impulse responses.

9. Conclusions Measuring the sound intensity allows us to obtain more information about the acoustic field around sources than just pressure information. Time and space information is very valuable and can be used, for example, in sound engineering and architectural acoustics. The development of low-cost methods of intensity measurement with sufficient accuracy is the basis for the dissemination of intensity methods in various fields of technology. The structures of p–p probes presented in the article fit well into this trend of development of measurement sensors. The sound intensity values are determined on the basis of a theoretical model. The accuracy of the determination of the direction of sound intensity is about 4 deg. The range of intensity measurement is limited from above by the maximum SPL value of the microphones used and for Sonion 8011 microphones the value is 112 dB SIL (Sound Intensity Level) (0.158 W/m2). The minimum value is limited by the noise level of the measuring system, the distance between the microphones in the probe, and the frequency range to be measured. The total noise level of the system is mainly influenced by the internal noise of the microphones, which for the Sonion 8011 used is 26 dB SPL. At this value the sensitivity of the probe is limited from below at 80 Hz by 72 dB SIL and at 1 kHz by 44 dB SIL. The proposed method requires from the user only a simple calibration of the measuring channels (particularly relevant for the two-microphone method). It is limited to determining their sensitivity using a standard electroacoustic calibrator with an appropriate coupler interface. At this stage of research the probe seems to be useful both for the measurement of properties of sound sources in the free field and of rooms in the diffusion field. In the future, we plan to use this method in two areas of application. The first one is the analysis of noise generated by electrical machines using various synchronization methods of data acquisition with the rotation phase of the machine’s shaft. The second application is the use of directional impulse responses of rooms for the spatialization of sound recordings using convolution method.

Author Contributions: W.M.: Overall concept of the measurement method, experiments and the article, data analyzes, writing the article; M.R.: creation of a measuring system, carrying out of measurements, data analyzes, writing the article; A.P.: design and realization of mechanical construction of mechatronic p–p probe. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Conﬂicts of Interest: The authors declare no conﬂicts of interest.

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