Sound Intensity and Its Measurement and Applications

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State of the Art of Sound Intensity and Its Measurement and Applications

Finn Jacobsen

Acoustic Technology, ØrstedDTU, Technical University of Denmark, Building 352, DK-2800 Lyngby, Denmark

The advent of sound intensity measurement systems in the beginning of the 1980s has had a significant influence on noise control engineering. Today sound intensity measurements are routinely used in the determination of the sound power of machinery and other sources of noise in situ. Other important applications of sound intensity include the identification and rank ordering of partial noise sources, visualisation of sound fields, determination of the transmission losses of partitions, and determination of the radiation efficiencies of vibrating surfaces, and recent work suggests the possibility of measuring sound absorption in situ using sound intensity. This paper summarises the basic theory of sound intensity and its measurement and gives an overview of the state of the art in the various areas of application, with particular emphasis on recent developments.

INTRODUCTION of the history of the development of sound intensity measurement is given in Frank Fahy’s monograph The most important acoustic quantity is certainly Sound Intensity [1]. the sound pressure. However, sources of sound emit The advent of sound intensity measurement sys- sound power, and sound fields are also energy fields tems in the 1980s has had a significant influence on in which potential and kinetic energies are generated, noise control engineering. Sound intensity measure- transmitted and dissipated. In spite of the fact that the ments make it possible to determine the sound power radiated sound power is a negligible part of the energy of sources without the use of costly special facilities conversion of almost any sound source, energy con- such as anechoic and reverberation rooms, and today siderations are of enormous practical importance in sound intensity measurements are routinely used in the acoustics. In ‘energy acoustics’ sources of noise are determination of the sound power of machinery and described in terms of their sound power, acoustic ma- other sources of noise in situ. Other important applica- terials are described in terms of the fraction of the in- tions of sound intensity include the identification and cident sound power that is absorbed, and the sound rank ordering of partial noise sources, visualisation of insulation of partitions is described in terms of the sound fields, determination of the transmission losses fraction of the incident sound power that is transmit- of partitions, and determination of the radiation effi- ted, the underlying assumption being that these prop- ciencies of vibrating surfaces. erties are independent of the particular circumstances. It is more difficult to measure sound intensity than This is not strictly true, but it is usually a good ap- to measure sound pressure. The difficulties are mainly proximation in a significant part of the audible fre- due to the fact that the accuracy of sound intensity quency range, and alternative methods based on linear measurements with a given measurement system de- quantities are vastly more complicated. pends very much on the sound field under study. An- Sound intensity is a measure of the flow of acous- other problem is that the distribution of the sound in- tic energy in a sound field. More precisely, the sound tensity in the near field of a complex source is far intensity I is a vector quantity defined as the time av- more complicated than the distribution of the sound erage of the net flow of sound energy through a unit pressure, indicating that sound fields can be much area in a direction perpendicular to the area. Although more complicated than earlier realised. The problems acousticians have attempted to measure this quantity are reflected in the extensive literature on the errors since the early 1930s it took almost fifty years before and limitations of sound intensity measurement and in reliable measurements could be made. Commercial the fairly complicated international standards for sound intensity measurement systems came on the sound power determination using sound intensity, ISO market in the beginning of the 1980s, and the first in- 9614-1 and ISO 9614-2. ternational standards for measurements using sound The purpose of this paper is to give an overview of intensity and for instruments for such measurements the status of sound intensity measurement, with em- were issued in the middle of the 1990s. A description phasis on developments from the past few years. MEASUREMENT PRINCIPLES AND mismatch errors ranging from 0.05° below 250 Hz to THEIR LIMITATIONS 1° at 5 kHz, which is slightly less than the maximum values specified in the IEC standard. There are essentially three methods of measuring It can be shown that the effect of a given phase sound intensity: i) one can combine two pressure error is a bias error that is proportional to the mean transducers (or more), ii) one can combine a pressure square pressure [7]. This implies that there is a limit to transducer with a particle velocity transducer, and iii) the amount of noise from sources outside the measure- one can use a microphone array. Each method has its ment surface that can be tolerated in sound power de- own limitations, but in addition there are some funda- termination using sound intensity, because such noise mental sources of error that do not depend on the mea- will invariably increase the surface integral of the surement principle [2, 3]. Array methods are used for mean square pressure and thus the bias error. reconstructing sound fields, including sound intensity. Another limitation of the measurement principle is This topic is outside the scope of this overview; see the restricted dynamic range at low frequencies: be- ref. [4]. cause the electrical noise of the microphones at low frequencies is amplified by the time integration needed in determining the particle velocity from the The two-microphone principle pressure gradient, one cannot in practice measure sound intensity levels below, say, 50 dB re 1 pW/m2 All sound intensity measurement systems in com- below 100 Hz [8]. mercial production today are based on the ‘two-micro- Other sources of error include the effect of air- phone’ (or ‘p-p’) principle, which makes use of two flow. Airflow gives rise to correlated noise signals closely spaced pressure microphones and relies on a that contaminate the signals from the two micro- finite difference approximation to the sound pressure phones. The result is a ‘false’ additive sound intensity gradient, from which the particle velocity is deter- at low frequencies [9]. mined. The IEC 1043 standard on instruments for the measurement of sound intensity deals exclusively with this measurement principle. The p-u measurement principle The finite difference approximation obviously implies an upper frequency limit. However, because of Attempts to develop sound intensity probes based the fact that the finite difference approximation error on the combination of a pressure transducer and a par- will be partially cancelled by a resonance if the length ticle velocity transducer have occasionally been de- of the spacer equals the diameter of the microphones, scribed in the literature [1]. A recent example is based the upper limit of the frequency range can be extended on the ‘microflown’ particle velocity transducer [10], to twice as much as suggested by the finite difference which is a micro machined hot wire anemometer. One error. Thus the resulting upper frequency limit of a problem with any particle velocity transducer, irre- sound intensity probe composed of half-inch micro- spective of the measurement principle, is the strong phones separated by a 12-mm spacer is 10 kHz [5], influence of airflow. Another unresolved problem is which is an octave above the limit determined by the how to determine the phase correction that is needed finite difference error when the interference of the when two fundamentally different transducers are microphones on the sound field is ignored [1]. An- combined (even though the influence of p-u phase other way of extending the frequency range is to apply mismatch will usually be less serious that the influ- a ‘sensitivity correction’ for the finite difference error. ence of p-p phase mismatch). Whereas one can com- Such a correction has recently been suggested for 3-D pensate for p-p phase mismatch by employing a simple intensity probes (without spacers) [6]; this also seems correction determined with a small coupler [7], there to double the upper frequency limit. is no similarly simple way of determining a correction Even with the best sound intensity measurement for p-u phase mismatch. systems available today the range of measurement is The measurement principle has the important ad- limited by small deviations between the phase re- vantage in sound power measurements that the perfor- sponses of the two measurement channels. Above a mance is not affected by the global pressure-intensity few hundred hertz the main source of phase mismatch index on the measurement surface, so in principle a is a difference between the resonance frequencies of larger amount of noise from sources outside the sur- the two microphones, which gives rise to a phase error face can be tolerated with p-u sound intensity probes that is proportional to the frequency. For example, one [11]. However, any such advantage has yet to be dem- must, with state-of-the-art equipment, allow for phase onstrated experimentally. APPLICATIONS Visualisation of Sound Fields

Some of the most important applications of the Visualisation of sound fields, helped by modern sound intensity method are now discussed. computer graphics, contributes to our understanding of radiation and propagation of sound and of diffrac- Sound Power Determination tion and interference effects [16] and has stimulated much research on sound fields [4]. Visualisation of One important application of sound intensity is the the flow of sound energy is particularly useful, with determination of the sound power of operating ma- obvious applications in noise source identification, chinery in situ. Sound power determination using in- and identifying and ranking noise sources and trans- tensity involves integrating the normal component of mission paths is the first step in practically any noise the intensity over a surface that encloses the source. reduction project. Near fields can be very complicated, The integral is usually approximated by scanning man- however. Johansson has examined various methods of ually or with a robot over the surface. Two interna- decomposing such near field intensity data into statis- tional standards are available, and a third one (for pre- tically independent components, using principal com- cision measurement) is on its way. ponent analysis and partial least squares regression A few years ago Paine and Simmons described the [17]. He concludes that a decomposition into principal results of an investigation of the uncertainties in the components enhances the identification of noise determination of sound power levels according to the sources. measurement procedures specified in various stan- One particular problem in using sound intensity in dards, including ISO 9614-1 [12]. The reproducibility identification of partial sources on vibrating structures standard deviation was found to be around 1 dB, and is the circulation of sound energy that occurs when the no indication of a systematic difference between the flexural waves on the structure travel slower than the standards was found. Nevertheless, Jonasson recently speed of sound. When the wavelength on the structure maintained that ‘it has long been suspected that this is shorter than the wavelength in air the waves do not standard....gives lower sound power levels than the radiate to the far field but may generate a circulatory other standards in the ISO 3740 series’ [13]. However, flow of sound power, out of the structure and back the only factor known to give a negative bias error in into the structure again in adjacent regions. To over- intensity-based sound power measurements is the ab- come the problems with such complicated near field sorption of the source under test, which reduces the phenomena Williams has introduced the concept of net sound power output. In fact, Jonasson’s observa- ‘supersonic intensity’ [4]. This quantity is defined as tion was based on preliminary results that have later the normal component of the part of the sound inten- been found to be affected by the absorption of the test sity associated with supersonic waves on the structure, source [14]. that is, waves that travel faster than the speed of sound. Eliminating the subsonic wave components Measurement of Transmission Loss does not affect the total radiated sound power of the structure, and, in the words of the author, ‘the credi- The intensity-based method of measuring transmis- bility of the concept of supersonic intensity lies in the sion losses of partitions was introduced in the early fact that power is conserved.’ The supersonic intensity 1980s as an alternative to the conventional method, is obtained by filtering out the subsonic wavenumber which requires a diffuse sound field in the receiving components from near field holographic data decom- room. It has often been reported that the intensity posed into wavenumber components, and in practice method gives lower values of the sound transmission this is only possible for structures of planar or cylin- index than the conventional method at low frequencies drical geometry. Pascal and Li have developed a re- and higher values at high frequencies. However, a crit- lated concept with similar properties called ‘irrota- ical examination of the literature has revealed that in tional acoustic intensity’ (since it has zero curl), de- most cases of poor agreement the receiving rooms fined as the gradient of the potential of the intensity have been very small [15], and a recent investigation [18]. Thivant and Guyader’s prediction tool ‘the inten- published in the same paper has demonstrated that sity potential approach’ [19] is closely related to the excellent agreement can be obtained in a fairly wide irrotational intensity. One cannot determine the super- frequency range, from 80 Hz to 6.3 kHz, provided that sonic intensity or the irrotational intensity with an or- the measurements take place in adequate facilities and dinary sound intensity measurement system; a are carried out with state-of-the-art equipment. holographic reconstruction method is needed. Other Applications 2. F. Jacobsen, J. Sound Vib. 128, 247-257 (1989). 3. F. Jacobsen, Applied Acoustics 42, 41-53, (1994). 4. E.G. Williams, Fourier Acoustics. Academic Press, San Ideally the ‘emission sound pressure level’ of ma- Diego, 1999. chines at specified positions should be measured un- 5. F. Jacobsen, V. Cutanda and P.M. Juhl, J. Acoust. Soc. der hemi-anechoic conditions; and corrections for Am. 103, 953-961 (1998). background noise and for the effects of reflections 6. H. Suzuki, S. Ogura and T. Ono, J. Acoust. Soc. Jpn. (E) should be applied when the environment differs from 21, 259-265 (2000). ideal conditions. Jonasson has proposed to determine 7. F. Jacobsen, Applied Acoustics 33, 165-180 (1991). emission sound pressure levels by measuring the 8. F. Jacobsen, J. Sound Vib. 166, 195-207 (1993). sound intensity instead of the sound pressure, the idea 9. F. Jacobsen, ‘Intensity measurements in the presence of being that the sound intensity would be less sensitive moderate airflow’ in Proc. Inter-Noise 94, Yokohama, Japan, 1994, pp. 1737-1742. to reflections from the surroundings than the sound 10. W.F. Druyvesteyn and H.E. de Bree, J. Audio Eng. Soc. pressure, which means that the troublesome environ- 48, 49-56 (2000). mental corrections could be avoided [20]. An interna- 11. F. Jacobsen, J. Sound Vib. 145, 129-149 (1991). tional standard is under development. Jonasson’s pro- 12. R.C. Paine and D.J. Simmons, ‘Measurement uncertain- posal is based on the assumption that the reflections ties in the determination of the sound power level of ma- that occur in a real room can be regarded as diffuse chines’ in Proc. Inter-Noise 96, Liverpool, England, noise, since ideal diffuse noise would not contribute to 1996, pp. 2713-2716. the sound intensity. Hübner and Gerlach have com- 13. H.G. Jonasson, ‘Noise emission measurements - System- atic errors’ in Proceedings of Inter-Noise 99, Fort pared several measurement procedures and seem to Lauderdale, FL, USA, 1999, pp. 1461-1466. favour determining the emission pressure level from 14. G. Hübner and V. Wittstock, ‘Further investigations to the maximum value of the sound intensity vector from check the adequacy of sound field indicators to be used three perpendicular components [21]. for sound intensity determining sound power level’ in Finally it should be mentioned that recent work Proc. Inter-Noise 99, Fort Lauderdale, FL, USA, 1999, suggests the possibility of measuring sound absorption pp. 1523-1528. in situ using sound intensity [22]. 15. M. Machimbarrena and F. Jacobsen, Building Acoustics 6, 101-111 (1999). 16. J. Tichy, ‘Visualization of sound energy flow and sound intensity in free space and enclosures’ in Proc. Interna- UNRESOLVED PROBLEMS AND FU- tional Symposium on Simulation, Visualization and TURE RESEARCH DIRECTIONS Auralization for Acoustic Research and Education, To- kyo, Japan, 1997, pp. 185-192. There are still a number of unresolved problems in 17. Ö. Johansson, ‘Sound intensity vector fields in relation to different reference signals’ in Proc. Fifth Interna- sound intensity measurement. tional Congress on Sound and Vibration, Adelaide, Au- As described above, there are essentially two fac- stralia, 1997, pp. 2255-2262. tors that limit the range of measurement with p-p 18. J.-C. Pascal and J.-F. Li, ‘Irrotational acoustic intensity: sound intensity probes, phase mismatch and electrical A new method for location of sound sources’ in Proc. noise from the microphones and preamplifiers. It Sixth International Congress on Sound and Vibration, should be possible to improve the performance of the Copenhagen, Denmark, 1999, pp. 851-858. conventional sound intensity probes in these respects. 19. M. Thivant and J.-L. Guyader, ‘The intensity potential If particle velocity transducers of sufficient stabil- approach to predict sound propagation through partial enclosures’ in Proc. Inter-Noise 2000, Nice, France, ity can be developed, the alternative p-u measurement 2000, pp. 3509-3514. principle would have a significant advantage in sound 20. H.G. Jonasson, ‘Measurement of sound pressure levels power determination in the presence of strong back- with intensity technique’ in Proc. Inter-Noise 93, ground noise, as pointed out above. Such probes Leuven, Belgium, 1993, pp. 363-366. would probably be too sensitive to airflow for many 21. G. Hübner, and A. Gerlach, ‘Further investigations on practical applications, but might on the other hand be the accuracy of the emission sound pressure levels deter- a very useful supplement. mined by a three-component intensity measurement procedure’ in Proc. Inter-Noise 99, Fort Lauderdale, FL, USA, 1999, pp. 1517-1522. 22. F. Jacobsen and L. Zamboni, ‘In-situ measurement of REFERENCES sound absorption using sound intensity’ in Proc. Eighth International Congress on Sound and Vibration, Hong 1. F.J. Fahy, Sound Intensity (2nd edition). E & FN Spon, Kong, 2001. London, 1995. Irrotational Acoustic Intensity and Boundary Values

J.-C. Pascala and J.-F. Lib

a Université du Maine, (LAUM UMR 6613 & ENSIM), rue Aristote, 72085 Le Mans, France b Visual VibroAcoustics, 51 rue d'Alger, 72000 Le Mans, France

The irrotational intensity corresponds to the non-vortex component of the active sound intensity. With the curl component eliminated, it can be used to characterize exactly `sources' and `sinks' regions on a complex radiator and to give more comprehensive behaviours of complex situations. By the use of processing data in wave number domain, the irrotational intensity can be computed from the 3-D standard sound intensity, which can be obtained by numerical calculations or from the technique of acoustical holography. Effects of source interferences on the field of the active intensity are evaluated and boundary values are studied. The use of the potential intensity field to predict sound fields from sources is discussed.

INTRODUCTION The field vector Ar of the active intensity contains all information on the sound intensity field. It can be The field of the sound intensity vector can be calculated in wave number domain by the use of 3-D decomposed into an irrotational component and a Fourier transform on the standard acoustic intensity curl component. The advantage of the irrotational in a whole volume [1] intensity [1] is the suppression of the well-known vortices in near field of radiation structures [2]. The IK * I r e j K rdr (3) D distribution of the normal component of the Performing this operation on the left and right hand irrotational intensity on a vibrating surface can sides of Eq. (2) yields provide us with the exact images of the sound power 2 2 2 2 2 of sources without sign fluctuations (positive and A K I K K with K K x K y K z (4) negative) due to the interferences among sources. The scalar potential and the vector potential can Another advantage of the irrotational component is respectively be expressed in terms of the field vector that it is the gradient of a scalar potential field, which A such that j K AK and C j K P AK . is the only quantity that depends on the sound power of the sources. This property makes it possible to compute the scalar potential of the active intensity IRROTATIONAL INTENSITY from the acoustic power of sources using software of ON PLANE BOUNDARIES calculating the diffusion by numerical methods (heat transfer FE). However, it is complicated to perform The behaviours of the standard and irrotational predictions of acoustic field from energy quantities intensity on a plane surface can better be understood because of the interferential nature of a sound field. with the help of the field vector A.

Radiation of vibrating surfaces - The scalar potential ACTIVE INTENSITY FIELDS in a field point r can be written by

1 I r nˆ A general Helmholtz decomposition of a vector field r 0 dS , with R r r (5) ** 0 can be applied to sound intensity and structural 2 S R intensity fields [3] Thus I r0 nˆ corresponds exactly to the acoustic P I I IC C , with C 0 (1) power density of the sources on S. For a vibrating plate, this quantity is always positive whereas the From this relation, a field vector function A can be normal component of the standard intensity presents introduced such that [4] changes of sign, which do not correspond to a correct 2 image of the sources. I A A P P A (2) The difference between the normal components of C the standard intensity and the irrotational intensity h

FIGURE 1. From left to right: standard sound intensity, field vector A, scalar potential and out of plane component of vector potential C of the sound field produced by a point source located at a distance h from the rigid plane S at kh . can be seen when both of them are expressed in terms of the field vector Ar R 2 R 2 R 2 2 Az Az Az I nˆ Az Rx 2 Ry 2 Rz 2 (6) R R 2 R 2 R 2 Ax Ay Az I nˆ A Rz RxRz RyRz Rz 2 Sources above a reflection plane - Consider a point source of a distance h from a rigid boundary. The FIGURE 2. Irrotational (left) and curl (right) interferences of the sound field depend on the value intensities of the same source as in Figure 1. of kh (k is the wave number). In Figure 1 is shown the field vector Ar calculated from the standard DISCUSSIONS intensity Ir by using Eq. (4). Calculating A Experimental method of the acoustic holography yields the scalar potential of which spatial makes it possible to compute the distribution of the distribution is independent of kh (thus of the irrotational intensity on a vibrating surface to obtain frequency). The kh value modifies only the initial the exact image of the sound power distribution on sources [1,3]. Another application relates to the power W of the source. In addition, the scalar 0 calculation of the scalar potential by solving the potential can be expressed by Poisson equation 2 w , where w is the . . sin 2kh 1 1 distribution of source power. The prediction of the r W0 1 / / (7) 2kh 0 4 R 4 R> 0 sound field obtained by calculating the irrotational intensity gives good quantitative results, in particular where R and R> are respectively the distances of by using finite element methods [5]. However, local the source and its image from a field point. The phenomena due to the interferences cannot be irrotational intensity calculated from corresponds represented without a complete definition of the field quantitatively to the radiated energy and does not vector A. show the spatial fluctuations due to interferences (Figure 2). Contrary to , the vector potential (there REFERENCES is only one tangential component because of axial symmetry) is very sensitive to kh values. It is 1. J.C. Pascal, J.F. Li, "Irrotational acoustic intensity: a new method for location of sound sources", 6th Int. evident that the curl intensity, which is derived from Con. Sound Vib., Copenhagen, 5-8 July 1999, 851-858. C , contains the information of directivity of the field 2. F.J. Fahy, Sound intensity (2nd ed.), E./F.N. Spon, 1995. (Figure 2). Since the field can be built by using an 3. J.C. Pascal, "Sources and potential fields of power flow image source, introduced symmetry leads to in acoustics and vibration", NOVEM, Lyon, 31 aug.-2 sept. 2000. In I nˆ IC nˆ 0 on S (8) 4. P.M. Morse, H. Feshbach, Methods of theoretical physics, McGraw-Hill, 1953. This shows that the effects of interferences due to the 5. M. Thivant, J.L. Guyader, "Prediction of sound using reflection plane cannot be described by these the intensity potential approach: comparison with boundary conditions on S. experiments", NOVEM, Lyon, 31 aug.-2 sept. 2000. Introduction of sound absorbing materials in the Intensity Potential Approach

M. Thivant, J.L. Guyader

Laboratoire Vibrations Acoustique, INSA de Lyon, 69621 Villeurbanne France

In industrial noise control issues, energy methods are often worth being used in the mid and high frequency range [1]: CPU costs are much lower than using integral methods, solutions are more robust, and one gets energy paths, which can indicate relevant design modifications. The Intensity Potential Approach derives from the local energy balance. A thermal analogy makes it possible to use standard Heat Transfer Solvers. The irrotational part of active intensity [2,3] is obtained, as well as the acoustic power through the apertures and the pressure level in the far free field. Previous work [3] showed the capabilities of this method for predicting sound propagation through rigid partial enclosures. This paper completes the Intensity Potential Approach by taking into account local absorption phenomena. Absorbing materials are described by thermal convection factors related to acoustic impedance. This model has been tested on several cases and shows good agreement with IBEM solutions. The method is also being applied to trucks engine noise prediction.

1. INTENSITY POTENTIAL at every points Q on the obstacle. G(Q) is the potential APPROACH -temperature- obtained when replacing all absorbing The Intensity Potential Approach aims to predict boundaries by rigid ones (6). Then, G(Q) must be acoustic energy transfer through apertures, as well as divided by the total injected power to get the its dissipation into acoustic shielding. Helmholtz normalized blocked potential g(Q). In the thermal decomposition (1) of the active intensity vector field analogy, (7) can be viewed as a convection relation. ε into rotational and irrotational parts, together with The surface convection factor H= g(Q) depends on ε power balance relation (2), leads to exact Poisson’s acoustic properties of the boundary via , and on equation (3) for the Intensity Potential ϕ. location of both the sources and the obstacle Q via r r r r r r g(Q). From a practical point of view, such varying I =Iϕ +IC =−gradϕ+rotC (1) r convection coefficients can be easily defined in heat transfer solvers. divI(M)=q0δ(M,M0) (2) 2. ESTIMATION OF ABSORBING ∆ϕ(M)=q0δ(M,M 0) (3) COEFFICIENT ε Where q is a point power source located in M and δ is 0 0 A theoretical expression can be derived for ε, based on the Dirac delta function. Previous studies [2,3] have the solutions of equivalent thermal and acoustic shown that irrotational intensity Iϕ is related to far field problems. Consider a non-directional acoustic source S energy transfer and to energy sources and sinks. On the of power π (S) radiating above a partially absorbing other hand, rotational intensity I describes local loops 0 C plane characterized by its impedance: and directivity patterns, but it does not affect global Z=ρ0c(R+jX) (8) energy balance. ϕ and Iϕ are fully determined once the correct boundary conditions are defined. (4) holds for a Where ρ0 is the mass density of the medium, c is the source of power πs distributed on a surface S. Far free speed of sound, and R and X are respectively the real field radiation can be taken into account through (5), and imaginary parts of the normalized impedance of the plane. written on a Rl-radius hemisphere. Rigid obstacle are s0(S) described by (6). This paper focuses on the validation θ of (7), which stands for absorbing obstacles. ∂ϕ πS ∂ϕ 1 = (4) =− ϕ(R l) (5) ∂ ∂ l Z n s n R I (Q) ∂ϕ ∂ϕ n =0 (6) − (Q)=εgϕ(Q,S)ϕ(Q) (7) ∂n ∂n Fig 1 - Intensity absorbed by an infinite plane ε is a coefficient related to acoustic impedance of the The net intensity absorbed by the plane at point Q can be written, using plane wave approximation: boundary surface. Theoretical expression for ε is π0 2 proposed in §II. Boundary condition (7) requires In(Q)= (1−ℜ(θ) )cosθ (9) 4πr2 preliminary calculation of the blocked potential G(Q) Q Where rQ is the distance between the source S and the 3. COMPARISON WITH I-BEM point Q, and |ℜ(θ)| is the modulus of the reflection coefficient defined by (10). Zcosθ−ρ0c ℜ(θ)= (10) Zcosθ+ρ0c An equivalent thermal problem can be defined, taking a heat source with the same power π0(S) and an image source |ℜ(θ)|²π0. We get the potential -or temperature- at Q, as well as the intensity -or heat flux: ϕ = π0 +ℜ θ 2 (Q) π (1 ( ) ) (11) Fig. 3 - Intensity map on the source and at the aperture - IPA. 4 rQ Figure 3 shows IPA results for a constant velocity ∂ϕ π 2 − (Q)= 0 (1− ℜ(θ) )cosθ (12) piston source radiating in a box with uniform ∂ 2 n 4πrQ absorption inside. On figure 4 is plotted the power For a rigid plane, ℜ(θ)=1, thus through the aperture computed by IBEM and by IPA. π The power of this source in the free field is plotted in ϕ(Q)=G(Q)= 0 (13) 2πrQ bold. Variations between both methods stand within G(Q) 6dB. One should notice that source velocity is the input g(Q)= = 1 (14) data for IBEM, which leads to important uncertainty on π0 2πrQ the injected power. However both methods predict ε Then derives from (7), (11), (12) and (14): similar changes of output power when either 2 (1− ℜ(θ) ) absorption or geometry is changed. ε(θ,Z)= 2πcosθ (15) (1+ ℜ(θ) 2) This coefficient ε, defining absorption condition (7) in the equivalent thermal problem, depends only on acoustic properties of the plane via ℜ, and on incidence angle θ. For diffuse fields one can use an average value of ε with respect to θ: π 2  +  ε = ε θ θ θ= 4πR  −tan−1( R² X²)  (16) θ ∫ ( )sin d 1  R²+X² + Fig 4 Output power versus frequency - left: <α>θ=0.4 - right: 0  R² X²  <α>θ=0.944 - bold: free field. solid: IPA - dot: IBEM For X=0, (16) becomes: 4. CONCLUSION π tan−1(R)  ε =4 1−  (17) A model is proposed for absorption in the Intensity θ R  R  Potential Approach. Comparison of IPA with IBEM ε Figure 2 shows both < >θ and the usual diffuse field shows good agreement. Computing time is much lower absorption coefficient <α>θ, defined by (18), versus with IPA than with IBEM. On the other hand, positions the real part of normalized impedance. Amplitudes are of sources, absorbing materials and apertures can be quite different because <α>θ links absorbed intensity to taken into account quite precisely. Therefore IPA incident intensity, where as <ε>θ links absorbed seems to be an interesting tool for vehicle and intensity to potentials g(Q) and ϕ(Q). Nevertheless machinery outdoor noise prediction. they have similar evolution and reach their maximum 5. ACKNOWLEDGMENTS for very closed values of R -respectively 1.51 and 1.56. This work is supported by Renault V.I. and the French Ministry of Research and Technology. 6. REFERENCES [1] Guyader, J.L., State of the art of energy methods used for vibroacoustic prediction, In Proceedings of 6th International Congress On Sound And Vibrations, Copenhagen, Denmark, 1999, pp. 59-84. [2] Pascal, J. C., Structure and patterns of acoustic intensity fields, In Proceedings of 2nd International Congress on Acoustic Intensity, CETIM, Senlis, France, 1985, pp. 97-104.

ε α [3] Thivant, M., Guyader, J.L., Prediction of sound Fig. 2 - Solid: < >θ. Bold: < >θ versus R -log scale. propagation using the Intensity Potential Approach: comparison with experiments, In Proceedings of NOise and + α = 8 {R 2− 2 ln(R+1)} (18) Vibration Energy Methods int. congress, Lyon, France, 2000. θ R R+1 R A Method to Minimize the Effect of Random Error when Measuring Intensity Vector Fields in Narrow Bands

Ö. Johansson

Engineering Acoustics, Division of Environment Technology, Luleå University of Technology, S-97187 Luleå, Sweden

The objective of this paper is to validate a method that minimises the time required for narrow band measurements of sound intensity vector fields. An experiment was performed in a reverberation chamber. The source under investigation was a radial fan and its outlets. Sound intensity was measured over a rectangular grid that contained 84 sub-areas. The measurement was repeated four times using different procedures for spatial integration. The measurement results were then post processed by principal component analysis The idea is that the information contained in a complete set of data, can be used for minimising the effects of random error in a specific position in the vector field. The result was analysed at several frequencies having different global pI-indexes. Comparison between measured and refined vector field confirmed that the method reduces the effect of random error and improves interpretation of the result.

measurement data, both in frequency and spatial domains, e.g. areas of sound radiation. The idea is that INTRODUCTION the information contained in a complete set of data can be used for minimising the effects of random error in a Measuring sound intensity vector fields in narrow specific position in the vector field. The validation was frequency bands over a large surface is time made by visual comparison between measured and consuming. To reduce random error in vector refined vector field at several frequencies, having estimates long averaging times are required especially different global pI-indexes. where there are large pressure intensity differences [1]. For source characterisation, however, the information contained in spectral data of high resolution is needed. Several methods for source location have been EXPERIMENTAL PROCEDURE presented. Non of the methods, however, is as straightforward, robust and refined as the sound The sound intensity [4] was measured over a planar intensity method. The objective of this paper is to grid in front of the cover of a radial fan and its out lets. validate a method that minimises the time required for Four measurements were conducted using, 30 or 10- narrow band measurements of sound intensity vector cm distances, and 4 Hz or 16 Hz resolution. The fields. The method is based on principal component intensity was measured in the frequency range 0 - analysis (PCA) and has been validated experimentally 3600 Hz, by a 3D-probe (B&K 0447) connected to an by studies on a relatively simple source in good FFT-based 8-channel measurement system (LMS acoustical conditions [2]. For further validation an CADA-X, front-end HP-Paragon). The probe was experiment was performed in a reverberation chamber calibrated using an acoustic coupler B&K 3541. The (T60=6-8s). The source under investigation was a radial residual pressure-intensity index varied between 18 - fan plus its outlets. Intensity was measured in “real- 24 dB (200–3600 Hz). To ensure true real-time time” over a rectangular grid that contained 84 sub- performance, the six microphone signals of the 3d- areas. The measurement was repeated four times using probe were sampled during the measurement various BT-products, at two different distances from sequence. The intensity vector field was determined by the source. The intensity estimates were further post post processing the sampled pressure signals processed by PCA, which is an iterative procedure (Hanning, 75% overlap). The time averaged active based on singular value decomposition [2,3]. PCA is intensity spectrum (t=1.5s) was estimated for each 2 used to detect correlated patterns in intensity sub-area (0.01 m ) in the plane grid (7x12). The spatial position of the probe was logged on a seventh channel. refined vector field, indicates a reduction of random Finally, the intensity data was processed by PCA. error. However, the result is not as good as in the By using an appropriate number of principal previous study [2], due to the large number of negative components, the remaining non-systematic varying signs in the normal intensity components. Negative data can be removed, i.e. reducing the effect of random intensity could be expected in a highly reverberant error [2]. The final result is visualised as principal field, but in several positions it is erroneous estimates. intensity vector fields (PIV) for different frequencies. These errors may be detected by analysis of the residues between the measured and refined vector field. By this procedure all sign-shifts found using 16 Hz resolution, were detected. Correction of detected RESULTS AND DISCUSSION sign errors improved the result and gave a better definition of the sound radiating surfaces. However, The following discussion is based on measurement measurements far from the source in a reverberation results at 30-cm distance from the fan cover. The room are not an ideal condition and make it difficult to results at 10-cm distance will be analysed and interpret the vector fields. The results at 10-cm discussed in the extended paper version. distance, which also will be compared with results The averaged sound intensity spectrum (normal using very long averaging times, will be used as a final component) has predominant peaks at 380, 756 and validation of the method. These results will be 1136 Hz. At these frequencies, the cover and its presented and discussed at the conference and in the outlets, is forced to vibrate by pressure fluctuations extended paper. related to the fan blade frequency and its harmonics. Remaining intensity is related to structural modes excited by the turbulent flow and noise from the electric motor. SUMMARY Changing the resolution from 4 to 16 Hz is expected to reduce random error by 50%, if averaging Rapid measurements of 3D acoustic intensity time is kept constant. The difference in random error vector fields require real-time performance of an FFT- was most easily seen as sign shifts of the intensity based measurement system. Real-time measurements component normal to the surface (from negative to were achieved by post processing the pressure signals, positive at 4 positions). Generally, the intensity vectors sampled during scanning. The effect of increased at the most important frequencies indicated large random error due to short averaging time was partly random errors. The effect of random error can be reduced by principal component analysis. The predicted on the basis of BT-product and the pI-index averaging time may be reduced by 75 % and still good [1]. For example, at 380 Hz the global pI-index is 10 estimates of the intensity vector field may be obtained. dB (756 Hz, 5dB; 1136 Hz, 6dB). This indicates The problem is to know the minimum time required severe measurement conditions, since the pI-index for an acceptable measurement quality. Ideally the may be very large at specific positions. The predicted procedure may be done automatically. The most normalised standard deviation at 380 Hz, based on the important benefits of the described method are the BT-product (B=4Hz, T=1.5 s) and the global pI-index limited time in front of the source, and the true real- (10dB), is 1.65 locally and 0.18 in relation to the total time measurement of the sound intensity vector field. averaging time (T=126s). The proposed method was tested on the measurement results based on 4 Hz resolution. Before PCA, measurement data was transformed, to obtain REFERENCES nearly normal distributed intensity data in both spatial and frequency domain. The absolute value of each 1. [1] F. Jacobsen Prediction of Random Errors in Sound amplitude estimate was power transformed (|I|0.25). Intensity Measurement. International Journal of Acoustics and Sign information was stored and added after PCA. Vibration, 5, No 4, 173-178 (2000). Another important requirement is that each variable 2. Ö. Johansson “Rapid Measurements of Acoustic Intensity (frequency component) is normalised (mean centred). Vector Fields”, Proc. of the 7th International Congress on PCA resulted in eight significant principal Sound and Vibration, Garmisch Partenkirchen 7-10 july 2000. components, which describe 59% of the variance in the transformed data matrix. However, at 380 Hz two 3. A. Höskuldsson, Prediction methods in science and technology, Vol 1. Basic theory. Thor Publish., Denmark, 1996 principal components explained 95% of the variance (756 Hz, 4 comp, 70%; 1136Hz, 4 comp, 23%). The 4. F. Fahy, Sound intensity, 2nd edition,. E & FN Spon, London, comparison between measured intensity and the 1995 $Q LQGLFDWRU EDVHG RQ PRGDO LQWHQVLW\ IRU WHVWLQJ WKH LQÀXHQFH RI WKH HQYLURQPHQW RQ WKH VRXQG SRZHU RI DQ DFRXVWLF VRXUFH

Domenico Stanzial4,DavideBonsi 7KH 0XVLFDO DQG $UFKLWHFWXUDO $FRXVWLFV /DERUDWRU\ 6W *HRUJH 6FKRRO )RXQGDWLRQ &15 ,VROD GL 6*LRUJLR 0DJJLRUH FR )RQGD]LRQH &LQL 9HQH]LD ,WDO\ KWWSZZZFLQLYHFQULW

A new indicator very sensitive to the room resonances excited by an acoustic source is here introduced and used as an environmental parameter for certifying the sound ¿eld condition when measuring the acoustic power of the source by the intensity method. This quantity will be called UHVRQDQFH LQGLFDWRU Thanks to its experimentally proved properties a de¿nitive insight of the physical meaning of the “oscillating intensity” as introduced in previous papers is accomplished. The results of a set of measurements of the sound power of a reference source in different acoustical environments will be presented and discussed using the introduced indicator.

,1752'8&7,21 to the equality kzwl3 the rate of energy absorption, in turn, must be equivalent to the integral of k+{>w,l The de¿nition of the acoustic power of sources is based over Y (stationary energy balance). Unfortunately, nei- on the well-known acoustic energy corollary which ther mathematical nor experimental handling de¿nition is demonstrated to be consistent with the requirement for +{>w, has been formulated yet, so the only way for of energy conservation in a Àuid to second order [1]. evaluating the acoustic power of a source must be based Within this theoretical frame, the power of an acous- on sound intensity: can be experimentally evaluated tic source can be expressed in terms of the stationary determining the time average vector ¿eld D+{, at some time-averaged radiant (active) intensity D+{, as discrete points { 5 V and then approximating the inte- ]] gral (see [2]). In this paper a careful experimental inves- 5 À ¿ D+{, q g { (1) tigation about the in uence of eld boundaries condition V on the measured power of a reference acoustic source ¿ where the integral is taken over a closed spatial sur- has been carried out and a new eld indicator account- face V bounding the volume Y which usually contains ing for the sound energy “trapped-in-the-average” in the the source. is a real quantity measured in Z @ standing waves (normal modes of the environment) ex- M v4whose sign can be positive for a radiating source, cited by the source itself has been usefully employed as negative for a dissipative or absorbing source (a sink) an environmental parameter for acoustically certifying and must be equal to zero when the integral of Eq. the source power measurement. 1 is derived from the homogeneus continuity equation 7KH UHVRQDQFH LQGLFDWRU zw um @3,wherez+{>w, and m+{>w, stand respectively for the instantaneous sound energy density and in- Following a reasoning similar to the one which led to the ghi tensity. In this paper only the case 3 will be con- de¿nition of the sound radiation indicator @ D@f kzl sidered. the resonance indicator will be here introduced as When a source is enveloped by V the continuity z um @ ghi P equation takes the inhomogeneous form w @ (2) +{>w, where is the SRZHU GHQVLW\ depending in gen- f kzl eral ERWK on the source and the environment. It is worth s ghi 5 noting that zw vanishes when a stationary time-average where P @ ku l (apart from a numerical factor) is is performed on it so that also its integral over any vol- the Hilbert-Schmidt norm of the sound intensity polar- ume (contained or not in V) is zero. This fact, often ization tensor [3].Inotherwords is de¿ned as the misunderstood, has an important physical meaning be- effective value of the PRGDO LQWHQVLW\ P normalized to cause tells us that when stationary energy conditions are f kzl thus representing the fraction of the energy density reached the time rate of the energy emission from the which is locally associated in the average to the normal source (i.e. the source power) must be equal to the time modes excited by the source. A preliminary analysis on rate of the energy absorption by the boundaries. Due a similar indicator can be found in Ref. [4]

Also with Cemoter-CNR, Ferrara, Italy 0($685(0(17 $1' 5(68/76 sources are needed, the two indicators and should be employed for certifying the inÀuence of the environment Figure 1 shows the reference source and the intensity on the measured ¿eld. This should be done optimally at probe used for measuring the sound power in two dif- every point where data for the power computation are ferent rooms. The ¿rst one is very “dead” due to the collected. 4 absorbing upholstery (W93 ? 43 v) while the second one is a normal room of the same volume and character- 80 ized by W93 * 4 v. The input signal to the source (white noise) and the enveloping surface (a sphere centered at 78 the top of the source having a radius of 4=8 p)werethe 76

same for the two measurement sets. )

d (

e w

o 72 P

66 125 250 500 1000 2000 4000 freq. (Hz)

),*85( : Values of sound power (squares: dead room, circles: normal room). 1 ),*85( : The source and a measurement point. Once ¿xed the equatorial plane parallel to the Àoors, 0.9 µ the radial component of sound intensity in two positions 0.8 2 78 78 7 <3 µ North and South belonging to meridians 0.7 1 apart for a total of ; points was measured. These data were then used for the power computation. We collect 0.6 data for evaluating at only one measurement point in 0.5 5 p η the equatorial plane at a distance of from the centre 0.4 1 of the sphere. 0.3 Figure 2 reports the calculated power of the source in the two rooms for third-octave bands ranging from 433 0.2 8333 K} η to . Figure 3 reports the comparison between 0.1 2 the indicators and , measured at one point in front of 0 the source in the two rooms. 125 250 500 1000 2000 4000 freq. (Hz) &21&/86,21 ),*85( :Valuesof and (squares: dead room, circles: normal room). According to the precision of our measurements the power of the reference source results slightly greater 5()(5(1&(6 (4 5 dB) for all bands when the source is radiating in the absorbing room. This can be considered an exper- 1. A.D. Pierce, $FRXVWLFV, pp. 36-39, ASA-AIP, 1989. imental evidence of the fact that the power of an acoustic 2. F. Fahy, 6RXQG LQWHQVLW\, Chapter 9, Chapman & Hall, source depends inescapably from the boundaries condi- London, 1995. tions or, stated in other words, that when the acoustic 3. D. Stanzial, N. Prodi, D. Bonsi, J. Sound Vib., 232(1), ¿eld feeds back to the source, the source itself becomes 2000, 193-211. a boundary condition for the acoustic ¿eld. For this 4. D. Bonsi, Ph. D. dissertation, University of Ferrara, reason, when accurate power measurements of acoustic 1999. Time-dependent Sound Intensity Measurement Methods H. Suzuki

Department of Network Science, Chiba Institute of Technology 2-17-1 Tsudanuma, Narashino-shi, Chiba-ken 275-0016 Japan

The most commonly used sound intensity is the time-averaged sound intensity. This method, however, is not suitable for the analysis of transient sounds. In this paper, two types of time-dependent sound intensities are introduced. The first one is the envelope intensity. The envelope intensity is obtained from the multiple of the analytic (with zero spectra at negative frequencies) time-dependent pressure and particle velocity. The envelope intensity gives a rather slowly varying intensity like the envelope of the signal. Since it has the directional information, it can be used for the localization of transient sound sources in the three dimensional space. The second method is the application of cross Wigner distribution to the sound intensity. This gives the sound intensity distribution on the time-frequency plane. Some application examples of the above two methods will be introduced.

INTRODUCTION xa (t) x(t) jxh (t) (3)

where xh(t) is the Hilbert transform of x(t). Information on the intensity and the direction of a A three-dimensional sound intensity probe shown in transient noise is important in order to understand its Figure1 was used for the measurement of the envelope generation mechanism and contrive a method to reduce intensity. The microphones are located at the apexes of or eliminate it. For example, a large glass window a tetrahedron. The pressure is the average of the four occasionally generates a transient noise when the pressure signals and the particle velocity components ambient temperature changes drastically. It is difficult, for x, y, and z axes are also calculated from linear however, to estimate from which part of the window combinations of the four microphone signals[3]. the noise is generated since the phenomenon is unrepeatable. Dozens of similar cases can be easily listed. In this paper, two sound intensity methods that can be used for the analysis of the transient sounds are reported. The first is the envelope intensity method[1] and the second is the "instantaneous sound intensity spectrum" method[2].

ENVELOPE INTENSITY FIGURE 1. Three-dimensional sound intensity probe

The instantaneous intensity is given by An example of the envelope intensity measurement is shown in Figure 2. An impact sound generated by i(t) p(t)v(t) (1) hitting a 900x900x9mm plywood from behind by a where p(t) and v(t) are the sound pressure and the small metal hammer was recorded in an anechoic room particle velocity in the direction of the measurement. by use of the probe shown in Figure 1. The top left and Even for a monotone sound, the instantaneous intensity right charts show the horizontal and vertical plane changes with twice of the original frequency. This is displays of the envelope intensity vector loci, the reason why the time-averaged intensity method is respectively. The analysis frequency band was from used for most of practical applications, which is 125Hz to 1kHz. Figure 2 shows that the direction of the unfortunately not suitable for transient sounds. The maximum intensity coincides with that of the impact envelope intensity was developed with a purpose of shown by the dotted line in the horizontal plane. The keeping the time dependency and still avoiding the middle and the bottom charts show x-, y-, and z-axis radical change of the instantaneous intensity. It is intensity components and the pressure of microphone 1 defined by as functions of time. * I e (t) Re[ pa (t)va (t)]/ 2 (2) where pa(t) and va (t) are the analytic functions of p(t) and v(t), respectively. The analytic function of x(t) is defined by FIGURE 3. Experimental setup for the measurement of a direct and reflected transient sounds

A result is shown in Figure 4. The horizontal and vertical axes represent the time and frequency, respectively. Arrows in the charts show the directions of the energy flow and the magnitudes as well as the time and frequency dependence. Several words shown in the box show possible reflectors for each wave packets. As this figure shows, it is possible to graphically represent frequency components of an instantaneous intensity by use of the cross-Wigner 0 time(ms) 160 distribution.

FIGURE 2. Envelope intensities and a pressure waveform of an impact sound generated by hitting a plywood

INSTANTANEOUS SI SPECTRUM The cross-Wigner distribution between p(t) and v(t) is defined by A W (t, f ) p*(t / 2)v(t / 2)e 2 f d pv *A (4) If p(t) and v(t) are given, respectively, by p(t) [ p1 (t) p2 (t)]/ 2 (5) 1 t v(t) * [ p (t') p (t')]dt' (6) d A 2 1 with pressure signals of two microphones of a p-p type one-dimensional intensity probe, p1(t) and p2(t), the instantaneous sound intensity spectrum (ISIS) is given by I(t, f ) Re[W p1p2 (t, f )]/ 2 f d (7) Figure 3 shows an experimental setup used for testing FIGURE 4. ISIS obtained from the setup shown in Fig.3. a usefulness of ISIS. A loudspeaker generated a 4-cycle 10 kHz sinusoidal tone burst and the direct and reflected sounds were recorded at the cross point of two arrows inside the region surrounded by three REFERENCES wooden boards.

1. Suzuki, H., Oguro, S., Anzai, M., and Ono, T, Inter-noise 91 Proceedings, Vol.2, 1037-1040 (1991). 2. Tohyama, M., Suzuki, H., and Ando, Y., The Nature and Technology of Acoustic Space, Academic Press, 1995, 143- 145. 3. Suzuki, H., Oguro, S., Anzai, M., and Ono, T, J.Acoust.Soc.Jpn, 16, 4, 233-238 (1995). Investigations into the correlation between field indicators and sound absorption

Gerhard Hübnera, Volker Wittstockb

a ITSM, Universität of Stuttgart, Pfaffenwaldring 6, D-70550 Stuttgart, Germany, [email protected] b PTB, Bundesallee 100, D-38116 Braunschweig, Germany, [email protected]

The sound power of a sound source measured by the intensity technique over an enveloping surface S may differ significantly from its true value if, in the presence of absorption within S, stronger directly incident background noises flow through this surface. The magnitude of this effect can be determined by a second measurement where the source under test is switched off and the background noise remains unchanged. This second measurement yields a negative sound power which directly describes the error of the first measurement if background noise and noise from the source under test are not correlated. Another approach is to check the presence of relevant sound absorption within S using the well-known sound field indicators. In principle, the global unsigned indicator and the global signed indicator, especially their difference, the sound field non-uniformity indicator and the difference between global indicators and the instrument‘s dynamic capability react to absorption inside S as they do to other influences. The paper deals with theoretical and experimental results of the correlation between different indicators and absorption within S.

1 INTRODUCTION b) the background noise randomly superposes the original sound field at the measurement positions. Intensity-based sound power determinations are As is known [1], sound field situations can be influenced by an additional error when an absorption described by certain sound field indicators which are is included in the measurement surface and stronger in particular the unsigned pressure intensity indicator extraneous noise sources are present. When the source F=L-L-K, (2) is switched off, with the background noise remaining pInp In 0 unchanged, the absorbed sound power Pabs can be the signed pressure intensity indicator determined which can be used to correct the measured F=L-L-K (3) sound power pInpIn 0 and the field non-uniformity indicator Ptrue=Pmeas+Pabs (1) N assuming that the source under test and the 11 2 FS=å( In,i-In) . (4) background noise are not correlated. InN-1I=1 Under practical conditions, however, it is Definitions of the several symbols are given for sometimes not possible to switch off the source under example by the Draft International Standard ISO test without changing the background noise. An 9614-3. The bar indicates the average value on the example of this is the sound power determination of measurement surface. The error due to absorption is one specific part of a machinery set. In such cases, it is PmeasæPabsö of interest whether one of the well-known sound field Dabs==ç1- ÷ (5) PP indicators [1] or a new one can be used to indicate and trueètrueø limit significant sound absorption effects. where Ptrue is the sound power of the source determined in the absence of absorption and Pabs is the 2 THEORETICAL CONSIDERATIONS absorbed sound power determined by the “zero test“, where the source under test is switched off and the The effect of absorption situated within the space background noise remains unchanged. Exclusion of all enveloped by the measurement surface S depends on other error sources and introduction of the sound the magnitude of the background noise during the power Pmeas, measured in-situ, using eq. (1), yields measurements. Here, two different cases can be -1 distinguished: æPabsö Dabs=ç1+ ÷. (6) a) the background noise enters directly from a strong èPmeasø parasitic sound source in close proximity to the With measurement surface, or IS levels between 0 and 10 dB. The absorption was Pabs n,zero 0.1( FpI+Fzero) /dB ==10 n , (7) caused by a plate (chipboard, 40 mm thick) forming P meas In,measS one of the boundaries of the measurement surface. the level of the absorption error follows to be For this practical approach the indicators æ0.1F+F /dBö ( pIn zero) (8) F-F and FS are regarded which can be LD,abs=-10lgç1+10÷dB pIn pIn èø determined under conditions where performance of the with the zero test indicator zero test is not possible. Figures 1 and 2 show the æö In,zero dependence of the absorption indicator on these two F=10lgçrc ÷dB. 9 zero ç2 ÷ indicators. For this specific example, the criterion èp%measø from eq. (11) is fulfilled if FS < 3 or < 1 or The magnitude of the indicator F comprises pIn F-F< 4 dB or < 0 dB. For other acoustical pIn pIn different influences such as the near field error, situations – for instance for semi-reverberant environ- environmental corrections and the noise-to-signal ments – other limiting values can be expected. ratio. This indicator cannot therefore be used for detecting the presence of background noise or of 20 absorption errors, only. Eq. (8) shows that for the F abs/dB criterion 10 limit determination of LD,abs both indicators, F and Fzero, pIn are necessary. Only if the measurement surface is 0 situated in a reverberant field region ( Fzero®-¥), -10 LD,abs is equal to zero. This means for measurements -20 outside the reverberant radius that the absorption 0,1 1 10 100 1000 inside S is simply added to the total room absorption. F S Furthermore, alternatively to Fzero, the indicator Figure 1 Indicator F as a function of F Pabs abs S Fabs=10lgdB. (10) Pmeas can be introduced which directly indicates the ratio of 20 F abs/dB criterion the absorbed sound power to that measured. Based on 10 limit the formula given above, the error due to the 0 absorption effect such as LÄ,abs£0.41dB or £0.14dB is limited by -10 FF=-F £-10dBor £-15dB. (11) abspIn zero -20 If the zero test cannot be carried out for practical 0 5 10 15 20 25 30 reasons, LD,abs can be determined or limited only (F p lI nl-F pI n)/dB approximately. Figure 2 Indicator Fabs as a function of F-F pIn pIn 3 PRACTICAL APPROACH 4 CONCLUSIONS An absorption error can of course be excluded if In order to check the significance of absorption effects, the noise-to-signal ratio vanishes. This can be tested the zero test should preferably be carried out. Results by determination of the difference of this test allow sound power corrections or calcula- F-F . (12) pIn pIn tions of the amount of the absorption error to be If this difference is zero, no significant background carried out. If the zero test cannot be carried out, noise is present. certain other criteria allow the error to be assessed Under in situ conditions, however, where a certain only approximately. background noise level and an unknown absorption exist, a procedure capable of limiting the absorption REFERENCES error is of interest. The data base of an earlier 1. G. Hübner, INTER-NOISE 84 Proceedings, pp. investigation [2] can be used for such an approach. 1093-1098 These investigations were carried out in a semi- 2. G. Hübner, V. Wittstock, INTER-NOISE 99 anechoic room with extraneous noise superelevation Proceedings, pp. 1523-1528

ISO standards on sound power determination by sound intensity method

a b H. Tachibana and H. Suzuki aInstitute of Industrial Science, University of Tokyo, Komaba 4-6-1, Meguroku, Tokyo 153-0041, Japan bDept. of Network Science, Chiba Institute of Technology, Tsudanuma 2-17-1, Narashino, Chiba 275-0016, Japan

The outline of ISO 9614-3 “Acoustics-Determination of sound power levels of noise sources using sound intensity-Part 3: Precision method for measurement by scanning” is introduced by comparing with the former two standards, ISO 9614-1 and 2.

INTRODUCTION Evaluate the temporal variability For the determination of sound power levels of indicator and determine T < sound sources using sound intensity method, we FT 0,6 have two ISO standards under the general title Define the measurement surface, “Acoustics - Determination of sound power levels partial surfaces and scanning path of noise sources using sound intensity”; ISO 9614 - Part 1 “Measurement at discrete points” and ISO Choose one partial surface 9614 - Part 2 “Measurement by scanning”. As the third standard of this series, ISO 9614 - Part 3: Determine the scanning time “Precision method for measurement by scanning” T = N ⋅T < S S FT 0,6 has just been drafted as an ISO/FDIS (as of February 2001). No

Is TS practicable ? Take action A MEASUREMENT UNCERTAINTY Yes See TABLE1. Perform two scans TABLE 1. Measurement uncertainty of ISO 9614-3 1/3 octave band Upper values of Crt. 1 Take action B − ≤ No center frequencies standard deviation of LIn(1) LIn(2) s / 2 [Hz] reproducibility [dB] Take action C 50 to 160 2,0 For all partial Yes surfaces 200 to 315 1,5 Crt. 2 No 400 to 5 000 1,0 L ≥ F 6 300 2,0 d pIn * A-weighted 1,0 Take action D or E * Calculated from third-octave bands from 50 Hz to 6,3 Yes kHz. Crt. 3 − ≤ No FpIn Fp In 3 MEASUREMENT PROCEDURE Yes Take action G The measurement surface is defined around the Scanning Yes source under test as shown in Fig.2. It is divided already increased? into several partial surfaces on which partial sound Crt. 5 power is determined by each scanning. No No 0,83 ≤ F / F ≤ 1,2 In the measurement by scanning, time-series of S(1) S(2) intensity and squared sound pressure are Crt. 4 ≤ No Yes continuously measured and stored using FS 2 Take action instantaneous mode of the instrument. From these F or G results, four kinds of field indicators, temporal Yes variability indicator: FT , field non-uniformity Final result indicator: FS , unsigned pressure intensity indicator: F , and signed pressure intensity FIGURE 1. Flow of the measurement in ISO 9614-3 p I n

surface (Crit.1), for the adequacy of the measurement equipment (Crit.2), for the presence of strong partial extraneous noise (Crit.3), for the field non-uniformity surface (Crit.4) and for the adequacy of the scan-line density 1 partial surface (Crit.5) are made as shown in Fig.1. If these requirements are not satisfied, actions to increase the Partial grade of accuracy are indicated. surface segment NORMALIZED SOUND POWER LEVEL ∆ y 2 0,83 ≤ ∆x / ∆y ≤ 1,2 To standardize the value of sound power level of a source, “normalized sound power level” L is ∆ W 0 x scanning path defined as the sound power level under the reference FIGURE 2. Measurement surface θ ° meteorological condition (temperature 0 =23 C , barometric pressure B =101,325 kPa), given by: indicator: FpIn shown in Table 2 are evaluated. 0   (Terminology in the former two standards, Part 1 and 2, = − B 296,15 LW 0 LW 15lg  dB is inconsistent and reconsidered in Part 3.) 101325 273,15 + θ  In order to guarantee the upper limits for measurement where, θ is the air temperature in °C during the uncertainties, check for the adequacy of the averaging actual measurement, B is the barometric pressure in time, for the repeatability of the scan on a partial Pa during the actual measurement.

Table 2. Field indicators used in 9614-1, 2, and 3 Indicator ISO 9614-1 ISO 9614-2 ISO 9614-3

Temporal M 1 1 1 1 M variability indicator = ∑ − 2 = − 2 F1 (I nk I n ) ― FT ∑(I n m I n ) M −1 = − I n k 1 I n M 1 m=1

Field 1 1 N 1 1 J non-uniformity = − 2 ― = − 2 F4 ∑(I ni I n ) FS ∑(I n j I n ) − = − indicator I n N 1 i 1 I n J 1 j=1

Surface pressure intensity Negative partial power Unsigned pressure-intensity indicator indicator indicator

= − = = − F L L F+ − 10lg[∑ P / ∑ P ] Fp I Lp L I 2 p In / i i n n Un- N N J 1 0,1L 1 2 2 = pi = = L = 10lg( ∑ p / p ) signed Lp 10lg( ∑10 ) Pi I ni Si P ∑ Pi p j 0 J = N i=1 i=1 j 1 N = − J 1 * F+/− F3 F2 in a special 1 Pressure = L = 10lg( ∑ I / I ) L I 10lg( ∑( I ni / I0 ) I n 0 n case. n J = j intensity N i=1 j 1 indicator Negative partial power Sound field pressure-intensity Signed pressure-intensity indicator index indicator

= − + = − F = L − L FpI [Lp ] LW 10lg(S / S0 ) FpIn L L 3 p In p In N  N  Signed 1 0,1L J = 1 = pi 1 LI 10lg( ∑ Ini / I0 ) [Lp ] 10lg ∑(Si10 ) = n LI 10lg ∑ I n j / I 0 N =  S i=1  n i 1 J j=1 N = = 2 S ∑Si , S0 1 m i=1 = * FpI F3 in a special case.

Sound Intensity Detection for Multi-sound Field Using Microphone Array System Based on Wavelength Constant Matrix K. Kuroiwaa and O. Hoshinob Faculty of Engineering, Oita University, 700 Dannoharu Oita 870-1192, Japan e-mail: [email protected] [email protected]

One problem with the traditional method of sound intensity is that it cannot give the individual sound intensity of interest in a multi-sound field. The objective of this study is to develop a sound intensity detection system for a multi-sound field. The proposed system consists of three-dimensionally spaced microphone array, sound detection filters based on wavelength constant matrix and sub-system of sound intensity estimation. A wavelength constant matrix is exactly formulated in terms of sound directions so that it can give a relation between the microphone outputs and the respective sound existing in a multi- sound field. Feeding microphone outputs to the filters, the system can issue the respective sound at the specified virtual points of our choice. Therefore, it can give three-dimensional vector of the respective sound intensity. Experiments of the incident and reflected sound intensities near the reflective panel for oblique incidence from 0 to 60 degrees in an anechoic chamber showed that the proposed system is fundamentally valid in sound intensity detection. The mean errors were 4.3 percents in amplitude and 5.1 degrees in direction in comparison with the original.

DETECTION OF SOUND INTENSITY A V B V. j2 i f m n / The block diagram of sound detection system is cmn (V,i) exp / (4) U B V 0 illustrated in FIGURE 1. In a multi-sound field, it is n assumed that there are N sorts of sound sources. The th n of sound source, Sn , shown with ‘filled circle’ with in which, U, f and raised dot denote sound velocity, coordinates (rn, n, n) radiates its original sound pn(t) frequency resolution in DFT spectrum and inner and the relevant sound intensity, In, shown with arrow product of two position vectors, respectively. Cv towards a microphone array located at the origin. The implies the wavelength constant matrix having the size th m microphone, Mm, with coordinates (dm, m, m) of N P M. receives all arriving sounds and issues the output of Substituting the position vector Vx of Mx for V in th qm(t) that alters in phase and magnitude depending Equation (1) and also V-x of M-x, then the n sound Pn upon the mutual situation given by the position vector (Vx,i) for Mx and Pn(V-x,i) for Mx can be estimated, A of M with m=1 M, B of S with n=1 N and respectively. Therefore, we can obtain the x-axis m m n n th position vector V of such virtual points as Mx and M-x component of n sound intensity In,x [2]. It has the indicated with ‘gray circle’ on XYZ axes. form of th i * Letting the k sample of the original sound pn(V,t) 2 1 Im Pn (V x , i) Pn (V x ,i) assumed at the virtual point expressed by position In, x (5) 2 V V i vector V and the microphone output qm(t) be pn(k) and x x i i th 1 qm (k), and also letting the i frequency component of the DFT spectrum of them be Pn(V,i) and Qm(i), where denotes the density of air. In the same manner th respectively, then the n sound Pn(V,i) at V can be as for In,x, the y-axis component In,y and the z-axis th detected by using the following equation [1]: component In,z are estimated. Consequently, the n sound intensity In can be obtained as follows: M Pn (V,i) H nm(V ,i) Qm (i) (1) I i I + j I + k I (6) n n,x n,y n,z m 1 where i, j and k imply unit vector of XYZ-axes, where, the FIR filter Hnm(V,i) is given as follows: respectively.

H (V,i) C 1. (2) nm V C c (V,i) (3) V mn FIGURE 2 Schematic diagram of the experiment.

FIGURE 1. Block diagram of the sound intensity detection system.

EXPERIMENTAL RESULTS

The schematic diagram of the experiment in an anechoic chamber is shown in FIGURE 2. It is the purpose of this experiment to detect the incident sound intensity, Ii (I1), coming from a loud-speaker S1 with the coordinates ( 1.5 m, 90 deg., i deg. ) and reflected sound intensity, Ir (I2), from the reflector. For this case, second sound source, S2 , with the coordinates ( 1.5 m, 90 deg., 180-i deg. ) implies the mirror image source of S1 with respect to the reflector. Results of the sound intensity detection for acryl resin hard board and urethane foam board are FIGURE 3 Experimental results of the sound illustrated in FIGURE 3. The filled arrows directed intensity detection. leftwards and rightwards imply the detected incident sound intensity, Ii, and the reflected sound intensity, Ir, REFERENCES respectively. The detected sound intensity is expressed with ‘^’ on it in this section. To evaluate the detection 1) K.Kuroiwa, “Multi-microphone system for sound accuracy, the incident sound intensity, Ii, measured by detection based on wavelength constant matrix”, J. removing reflector is also illustrated with gray arrow. Acoust. Soc . Jpn.(E) 19, 289-292 (1998). It is shown that the proposed system worked well over 2) F.J.Fahy, 'Measurement of acoustic intensity using the incident angle from 0 to 60 degrees. Mean errors cross-spectral density of two microphone signals', were 4.3 % in magnitude and 5.1 degrees in direction. J.Acoust.Soc. Am. 62, 1057-1059 (1977). Free Field Measurements in a Reverberant Room Using the Microflown Sensors W.F. Druyvesteyn, H.E. de Bree and R. Raangs

University of Twente, postbus 217, 7500 AE Enschede, The Netherlands; [email protected]

Free field measurements in a reverberant room using the microflown sensors are described. The microflown is a sensor which does not measure the pressure, but the particle velocity in a sound field.

2 2 2 INTRODUCTION u// =ud + 1/3urev. The factor 1/3 comes from the integral over all angles in a sphere, representing all the The microflown is a sensor that measures the image sources, contributing to the diffuse reverberant particle velocity in an acoustic disturbance [1]. It field: (1/ 4 )* 2 sin( ).cos( ).cos( )d 1/ 3 . When consists of two heated wires; the particle velocity is 0 determined from the differential resistance changes in a second experiment the microflown is oriented such [1]. When a microflown sensor is combined with a that n is perpendicular to the free field velocity of the pressure microphone an intensity probe is obtained. sound source, the r.m.s. value is given by: u2 = Experimentally such a (simple) p-u intensity probe 2 2 2 1/3urev. . So by subtracting u// - u the free field is has been tested and found to be as good as the obtained. Two recordings have been made of speech in existing p-p intensity probes [2]. Main advantages of a reverberant room, one corresponding to u// and the the p-u probe above the p-p probe as intensity probe other corresponding to u. When reproducing these are that errors (or uncertainties) in the phases do not recordings a clear difference is heard: the recording of lead to large errors in the estimated intensity, and u contains only the reverberant sound field. The that one probe configuration can be used for a broad recordings will be reproduced during the presentation at frequency region (the p-p probe use different the conference. configurations for the low- and high frequency region). A disadvantage of the p-u probe can be that the calibration of the two sensors with respect to Two microflowns perpendicular to each each other is more difficult. other An important property of the microflown is its directional characteristic. Denote the orientation of The contribution of a pure diffuse reverberant sound the microflown by a vector n[x,y,z], which is defined field to the cross-correlation of two microflowns as follows. The vector n is in the plane through the perpendicular to each other, vanishes. To show this, two conducting wires of the microflown and consider the two dimensional case with two perpendicular to the length of the wires (the microflowns, having n-vectors n1 = [1,0] and n2 = [0,1]. maximum sensitivity of the microflown is when the Suppose two uncorrelated sound sources with power particle velocity is parallel with n). When the strength s1 and s2 are oriented in perpendicular direction of the particle velocity makes an angle directions, e.g. one under an angle with the x-axis, with n, the measured output of the microflown is and the second one having an angle + /2 with the x- proportional to cos( ), see [1] and [2]. This property axis. When the output signals of the two microflowns makes it possible to obtain free field ( no contribution are u1(t) and u2(t), the long term value of the cross- of reflections) properties of a sound field in a correlation Ru1.u2(0) is written as: reverberant environment. T Ru1.u2(0) (1/ T )* u1(t).u2*(t).dt 0

One microflown ; the symbol (0) in Ru1.u2(0) refers to the fact that no time difference is taken between u1(t) and u2*(t). The Consider the case that a sound source ( a loudspeaker contribution of source s1 is proportional to –cos( )*(- to which random noise is applied) is placed in a sin( )) and of source s2 to sin( )*(-cos( )); a positive reverberant room. When the microflown is oriented signal is assumed when the components of the such that n is in the direction of the free field particle connection vector r from source to sensor are in the velocity of the sound source the r.m.s. value follows positive x- or positive y-direction. When the strength of from the square root of the squared free field- and the two uncorrelated sources are equal, s1 = s2, the reverberant particle velocity: contributions to Ru1.u2(0) are equal but with different measuring the different sound quantities at almost the sign, thus Ru1.u2(0) vanishes. To verify this same point. A photograph of such a device is shown in experiments have been done with two sound sources figure 2. (loudspeakers) perpendicular to each other and with = 45 0. The loudspeakers were excited with two p uncorrelated noise signals within a frequency band of 900 – 1100 Hz. The results of the experiments are shown in figure 1, where is plotted R*u1.u2(0) as a function of the ratio’s of the power strengths s2/s1; R*u1.u2(0) being the normalized Ru1.u2(0) value with uy respect to the Ru1.u2(0) value at s2 = 0. The crosses (+) are the experimental results. For s2/s1 =1 the cross ux correlation is zero. uz

1.5 1mm

0.5 Figure 2. A photograph of the ux-uy-uz-p sensor. 0 u1.u2 *

R Information of the direction and the strength of a sound -0.5 source in an arbitrary direction can be found from the determination of the six possible cross-correlations. As -1 was explained above the diffuse reverberant sound field

-1.5 does not contribute to each of the possible six cross- 0 0.5 1 1.5 2 2.5 correlations. On the other hand the reverberant field s2/s1 does contribute in the four auto-spectra’s. Some Figure 1. The value of the cross correlation Ru1.u2(0) experimental results are shown in table 1. The normalized to the value at s2 =0 as a function of the abbreviations I refers to the found intensity in the x- ratio of the power strengths s2/s1 of the two sound x sources. direction, Rux.uy to the cross-correlation between the signals from microflown with nx = [1,0,0] and ny = In a pure diffuse reverberant sound field the [0,1,0]. The direction of the sound source was [0.43,0.41,0.50]. contribution of an image source to Ru1.u2(0) is always compensated by the contribution of another image Table 1. Results using the ux-uy-uz-p sensor. source in a perpendicular direction. Intensity Experimental Calculated measurements have also the property that the Ix/Iy 1.05 1.04 contribution of a diffuse sound field vanishes. So free Ix/Iz 1.05 0.85 field measurements in a reverberant environment can Rux.uy/Rux.uz 1.11 0.82 be done using an intensity p-u (or p-p) probe or using Ruy.uz/Rux.uz 0.98 0.96 two microflowns oriented in perpendicular directions. An important difference is of course that with two ACKNOWLEDGEMENTS microflowns perpendicular to each other one measures the product of two perpendicular The authors whish to thank the Dutch Technology components of the free field particle velocity vector, Foundation STW for the financial support. while with the intensity the free field product of p and u, being the energy flow. REFERENCES

Three microflowns combined with 1.H.E. de Bree, The Microflown (book) ISBN 9036515793; a pressure microphone www.Microflown.com (R&DBooks). 2. W.F. Druyvesteyn, H.E. de Bree, Journal Audio Eng. Soc. 48, 49- 56 (2000); R. Raangs, W.F. Druyvesteyn and H.E. de Bree 110th A more sophisticated device is to combine one AES Convention Amsterdam 2001, preprint 5292. pressure microphone with three microflowns oriented in perpendicular directions, e.g. n1 = [1,0,0], n2 = [0,1,0] and n3 = [0,01]. The four sensors are quite small and are positioned close to each other, thus Experimental Study on the Accuracy of Sound Power Determination by Sound Intensity Using Artificial Complex Sound Sources

H. Yanoa, H. Tachibanab and H. Suzukic

aDepartment of Computer Science, Chiba Institute of Technology, Tsudanuma 2-17-1,Narashino,275-0016,Japan bInstitute of Industrial Science, Univ. of Tokyo, Komaba 4-6-1, Meguro-ku, Tokyo, 153-8505, Japan cDepartment of Network Science, Chiba Institute of Technology, Tsudanuma 2-17-1,Narashino,275-0016,Japan

In order to examine the measurement accuracy of the scanning sound intensity method for the determination of sound power levels of sound sources, a basic experiment was performed using an artificial complex sound source. As a result, it has been found that the scanning method specified in ISO/FDIS 9614-3 provides almost the same results as those by the discrete method specified in ISO 9614-1 and the field indicators can be evaluated during the scanning using a running signal processing technique.

INTRODUCTION room (4m x 6.9m x 7.6m), in which the sound sources were placed as shown in Figure 1 at the center position As the third standard of ISO 9614 series, the on the reflective floor. As shown in the figure, the precision method for the determination of sound power measurement surfaces for each sound sources were set levels of sound sources by scanning sound intensity and sound intensity measurement was performed in 1/3 methods is now being drafted in octave bands from 100 Hz to 5k Hz by the scanning ISO/TC43/SC1/WG25 (DIS stage as of June, 2001). method and the discrete point method (12.5 cm mesh). For this work, some experimental studies were The measurement by manual scanning was performed performed on the measurement accuracy. In this paper, in two scanning patterns on each partial surface by an experimental study on the accuracy of sound power keeping the scanning speed at about 25 cm/s. In a determination by sound intensity under the condition successive scanning on each partial surface, both data where strong extraneous sources exist is introduced of sound pressure and sound intensity were obtained at and the validity of the field indicators are discussed. the same time at a sampling rate of 0.5 s. As the instrumentation, a pair of 1/2 in. condenser EXPERIMENTS microphone (B&K 4181) with 12 mm spacing and digital real-time analyzer (B&K 2133) were used. The As the sound source under test, the following three field indicators specified in ISO/DIS 9614-3 were kinds of sources were used and driven by different calculated automatically in a desk-top computer. random noises, respectively.

Source-1 “CAN”: a steel box to which an electric-shaker source 1:CAN source 2:BK4205 source 3: 8SP is attached. 0.75 m 0.75 m 1 m

Source-2 “BK 4205”: a loudspeaker-type reference sound source.

Source-3 “8SP”: a wooden

box in which 8 loudspeakers 1 m are equipped.

The measurement was performed in an hemi-anechoic

FIGURE 1. Configuration of artificial sound sources and measurement surfaces 80 80 80 CAN BK4205 8SP scan, simultaneous scan, individual

70 70 ) 70 discrete, simultaneous dB (

PWL (dB)PWL 60

scan, simultaneous 60 PWL 60

PWL (dB) (dB) PWL scan, simultaneous scan, individual scan, individual discrete, simultaneous disctrete, simultaneous 50 50 50 125 250 500 1000 2000 4000 125 250 500 1000 2000 4000 125 250 500 1000 2000 4000 frequency (Hz) frequency (Hz) frequency (Hz) FIGURE 2. Measured results of PWL 5 5 14 CAN scan, simultaneous BK4205 scan, simultaneous scan, simultaneous 4 4 scan, individual 12 8SP scan, individual

scan, individual | | 10

discrete,

In 3 In 3 | | | simultaneous

p 8 p In

2 discrete, simultaneous 2 | -F -F p 6 F - pIn 1 pIn 1 4 F F pIn

0 0 F 2 discrete, simultaneous -1 -1 0 125 250 500 1000 2000 4000 125 250 500 1000 2000 4000 125 250 500 1000 2000 4000 frequency (Hz) frequency (Hz) frequency (Hz) FIGURE 3. Measured results of field indicator: F F pIn p In

5 5 scan, simultaneous 25 scan, simultaneous BK4205 scan, simultaneous 4 CAN discrete, simultaneous 8SP F discrete, simultaneous 4 20 discrete,simultaneous scan, simultaneous scan, individual

scan, individual 3 3

s 15 s s F F 2 2 F 10 1 1 5 0 0 0 125 250 500 1000 2000 4000 125 250 500 1000 2000 4000 125 250 500 1000 2000 4000 frequency (Hz) frequency (Hz) frequency (Hz) FIGURE 4. Measured results of field non-uniformity indicator:Fs

RESULTS the value of FS exceeded the criteria (2 dB) in almost all frequency bands under “simultaneous” condition, Figure 2 shows the sound power levels of the three the measurement result of sound power level is in good sound sources measured by the scanning method and agreement with the result measured under the the discrete point method under the two operation “individual” condition. conditions; “individual”- each source was driven individually and “simultaneous”- all sources were CONCLUSION driven simultaneously. In the results of “simultaneous”, it is seen that the results obtained by As a result of the basic experimental study the scanning method and the discrete point method are mentioned above, it has been found that the intensity in good agreement over all frequency bands. To scanning method provides an accurate sound power compare the results measured under the two source level even under the adverse condition with strong operation conditions, the result for “individual” and extraneous noises. “simultaneous” are fairly in good agreement in every sound source not being influenced by the mutual REFERENCES intervention. 1. ISO 9614-1, -2 and DIS 9614-3 Figures 3 and 4 show the values of F F pIn p In 2. H. Yano, H. Tachibana and H. Suzuki, Proc. of 16th. I.C.A., 1998, pp.1461-1462 ( F3 F2 in 9614-1) and FS (F4 in 9614-1), respectively, measured under the two source operation 3. H. Tachibana and H. Suzuki, “ISO standards on sound conditions. In the case of the source 8SP, although the power determination by sound intensity method”, Proc. value of F F exceeded the criteria (3 dB) and of 17th. I.C.A., 2001 pIn p In Approximate Calculation of Sound Intensity Radiated through an Aperture from a Source in a Room

Y. Furue, K. Miyake and K. Konya

Department of Architecture, Fukuyama University, Hiroshima 729-0292, JAPAN

The purpose of this work is to develop a technique to calculate approximately the sound intensity field by acoustic radiation through an aperture from a sound source in a room. In this method the sound field outside of the room is assumed to consist of diffracted waves by the aperture of the direct sound from the source and of the diffused one in the room. Both Kirchhoff’s diffraction formula for the sound pressure and its derivative form for the particle velocity are applied to calculate the sound intensity owing to the direct sound from the source, while for the diffused sound in the room it is supposed for the sound to radiate from the aperture according to Lanbert’s cosine law. Numerical examples are presented with the measurements.

INTRODUCTION

In order to calculate exactly the sound intensity field q by acoustic radiation through an aperture of a room in which a sound source is located, we have to solve a Ps P P certain integral equation whose unknown function is Ps the velocity potential or sound pressure on the boundary surface. Such an integral equation method should be applied to calculate the sound field diffracted by any FIGURE 1. Model room with an aperture (left) and calcula- object whose dimension is comparable to the wave- tion model for direct component(right) length concerned. [1] In a very large room as compared to the wavelength, where(q) is the velocity potential at point q on A, r is the integral equation method to calculate the sound the distance from point P to point q and nq is the out- field is not applicable because of limitations in com- R R ward normal at q. Both (q)and (q)/ n q in Eq.(1) puter capacity or difficulties of determining the bound- are generally unknown. They must consist of the direct ary conditions. wave from the source and reflected ones by the room In this case an approximate approach based on surfaces. Those waves might be assumed incoherent Kirchhoff’s diffraction formula [2] becomes more with each other. practical. This formula requires both the velocity po- The sound intensity at P, I(P), could be divided into tential and its normal derivative on the aperture, which two parts, the direct component I (P) and the re- are unknown. These unknowns are assumed to consist dir flected one I (P). I(P) is the sum of those vectors. of the direct wave from the source and the diffused ref waves. The latter ones are assumed to make a surface I (P) I (P) I (P) (2) source at the aperture which radiates the sound to the dir ref outside of the room according to Lanbert’s cosine law. Calculation of the direct component

THEORETICAL BASIS The velocity potential and its normal derivative at point q on the aperture are given by We consider the situation where an n omnidirectional point source (Ps) is located in a room with an aperture (q) exp(iks) /s (3) and a receiving point (P) is outside of the room as and shown in Fig.1. Under Kirchhoff’s boundary condi- R (q) iks 1. /exp(iks) cos(s,n ) , (4) tions, the velocity potential at point P, (P) , is given by R 2 0 q n q s $ R . R .4 where s is the distance from Ps to q. 1 exp(ikr)/ (q) exp(ikr)/ (P) ** % (q) 5dsq (1) The direct component of the velocity potential at P is A R 0 R 0 4 & nq r nq r 6 expressed by: $ R . where denotes the air density, c the speed of sound 1 exp(iks) exp(ikr ) / dir (P ) ** % 4 A & s Rn r 0 and k wave number. Then the intensity of normal di- q rection at point q (I (q)) is given by means of geomet- iks 1. exp(ikr).4 n /exp(iks) cos(s,n ) /5ds (5) rical acoustic theory as follows, s2 0 q r 06 q W (1 ) In (q) (10) where is the The particle velocity at P, u(P), is given by: A average absorption coefficient and A the absorption area of the room. u(P) grad dir (P) Let Iref,x(P) the sound intensity for x-direction at R (P) R (P) R (P) . dir , dir , dir / (6) point P by above surface source, we obtain R x R y R z 0 cos Iref ,x (P) I n( q) ** 2 cos(r, x)ds , (11) also where A r R (P) 1 $R (q) R exp(ikr) . Iref,y(P) and Iref,z(P) similarly. dir ** % / R A R R 0 x 4 & x nq r R 2(q) exp(ikr) .4 NUMERICAL SAMPLES /5ds (7) R R 06 q x n q r AND MEASUREMENTS

Let Idir,x the sound intensity for x-direction at P, A model room which has a rectangular aperture $ R (P) .4 I Re%p(P) dir /5, (8) (45cm x 45cm) was set in an anechoic chamber. The dir,x R & x 06 room which size is 600 x 600 x 900cm is made of plywood board 12mm thick. A third octave band noise where p(P) i dir (P) is the complex conjugate of the sound pressure at P. was used as the source signal and the location of the source is the center of the room. Similarly we can calculate Idir,y and Idir, z and we ob- Sound intensity was measured by means of 4- tain the sound intensity of the direct component by microphone system (ONO SOKKI Co.) and measure- summing up those vectors. ment points were set near the aperture. The numerical examples and the corresponding Calculation of the reflected component measurements at 2 kHz are shown in Figure 4 in sound intensity level. We suppose that the sound in a room is diffused after The approximate calculation method of the sound the first reflection and a surface sound source is made intensity field mentioned above might be applicable. at the aperture from which the sound is radiated according to Lambert’s cosine law. Calculated Measured

A -10

-20 dS q ƒÆ Inq

1 1325374961738597109121132 r, x x P FIGURE 4. Calculated and measured example.

FIGURE 3. Calculation model for reflected component REFERENCES When the volume velocity of an omnidirectional point source is unity, its acoustic power (W ) is given: 1. Y. Furue, Applied Acoustics 31, 133-146, (1990) 2. M.Born and E.Wolf, Principles of Optics, 4th ed., W 4 ck2 (9) Pergamon Press, Oxford, (1970) A Code for Computation and Visualization of Sound Power Measurements based on the ISO 9614-1 International Standard

E. Pianaa, G. Pianab and A. Armanic

aDipartimento di Ingegneria Meccanica, Università degli Studi di Brescia Via Branze 38, I-25123 Brescia, Italy, e-mail: [email protected] bAnalisys, Via Monte Rosa 1, I-25069 Villa Carcina, Brescia, Italy, e-mail: [email protected] cSPECTRA srl, Via Ferruccio Gilera 110, I-20043 Arcore, Italy, e-mail: [email protected]

Acoustic Intensity Data Analysis software has been developed with the two fold objective to calculate sound power of a source from intensity measurements and to allow a 3D representation of both the source outer surface and the map of interpolated results on the measuring grid. The code complies with the prescriptions of ISO 9614-1 and is particularly helpful when one of the field indicators specified in the ISO standard does not satisfy the necessary requirements so that measurements must be repeated by successive refinements of the measurement grid and, therefore, the computation may be rather time consuming. The code im- ports intensity data from several types of analyzers and computes the sound power level for each surface and each frequency complying with the ISO 9614-1 flowchart. The calculation procedure includes the treatment of one-octave as well as one-third- octave band data. It also performs a three dimensional visualization of pressure and intensity fields on the measurement surface by colour contour plots. The possibility of drawing three dimensional objects inside the measurement surface and the real time acquisition of FFT intensity spectra makes the program suited for research and development purposes.

INTRODUCTION 3D EDITING AND REPRESENTATION

F.J. Fahy has proved that sound intensity measure- In order to start a new project, the first step is to de- ment is one of the most effective techniques to deter- fine the geometry of the measurement surface and the mine sound power level and to perform a mapping of structures contained inside and outside it. Basic tools the major sources contained within a measurement sur- for editing the geometry are already implemented in face, as discussed in [1]. The international standard Acoustic Intensity Data Analysis (AIDA) package. The ISO 9614-1 [2] provides practical guidelines to achieve program can represent two different kinds of objects: this aim and requires the calculation of different indi- frames and measurement surfaces. Frames are the rec- cators giving information about the quality of the de- tangular elements used to represent the source and the termination and hence the grade of accuracy: F1 (tem- environment around it: equipment, bench, floor, walls, poral variability indicator), F2 (pressure-intensity indi- etc. Measurement surfaces are the rectangular elements cator), F3 (negative partial power indicator) and F4 used to represent the set of segments surrounding the (non-uniformity indicator). If one of the field indica- sound source. Each segment defines a measurement tors does not meet the requirements, the test procedure position. The user can draw several surfaces and put should be modified. Moreover the Standard suggests them together to build a more complex one. The pro- also to check two criteria related to the adequacy of the gram provides a 3D graphical representation of the measurement equipment and to the adequacy of the ar- sound power level over each surface (Figure 1). It also ray of measurement positions. All the tests must be provides a numerical listing and ranking of the sound performed for every single set of measurements on power levels coming from each one of them (Figure 2). each measurement surface used. Finally a table and a The user can represent pressure and sound intensity flowchart specify the actions to undertake if the chosen levels in three dimensions for both CPB and FFT measurement surface does not comply with the stan- analysis (up to 30 bands). Another important feature is dard requirements. The data to be collected are the the simultaneous visualization of more than one 3D pressure and sound intensity levels in octave or 1/3 surface, so that the user can check the source behaviour octave bands, whether they come from a CPB or from in different frequency bands at the same time. Different an FFT analysis. easily customizable colour scales are available. CALIBRATION

The program performs several types of calibration procedures to set up the gain of the microphones and to determine the pressure - residual intensity index. At the same time it is also possible to perform a phase correction for the entire apparatus. A phase correction is useful for FFT based measurements, when the operator wants to make a software correction of the equipment response. All the data coming from the calibration procedure are stored in a database where the user can re- FIGURE 2. Sample of numerical and graphical output showing measurement surface ranking and 1/3 octave band trieve the correct probe type and verify the calibration analysis. history of the transducers. The last calibration performed is automatically taken into account to check the instant suggestions of the necessary actions the user ISO 9614 – 1 field indicators and criteria. should consider in order to meet the Standard requirements. The real-time acquisition procedure enables the user to choose the sequence he wants to use to perform REAL-TIME PERFORMANCES the measurements. Alternatively, a direct access to any point of the measurement surface is also possible. The program can show pressure and intensity levels Moreover, a table gives a comprehensive insight of the from the OROS 25 power pack. In this case octave and field indicators computed for each measurement sur- 1/3 octave bands are synthesized directly from the FFT face. The possibility of drawing three dimensional ob- spectra. The real-time performance of the system en- jects inside the measurement surface and the linking ables the program to show and import directly pressure with virtually any FFT analyzer makes the program and intensity data from the analyzer, thus allowing suited also for research and development purposes. real-time computation of the sound power level radiated by the sound source through the probe remote control. Real-time analysis and visualization of data SOUND POWER DETERMINATION can be performed for the pressure levels, for the intensity levels and for the pressure – intensity index. Of If the ISO 9614-1 requirements are fulfilled, then the course the user can set up directly the analyzer from final result is within the selected grade of accuracy. the AIDA software choosing between linear and expo- The Sound Power levels are calculated and displayed nential averaging, number of averages, coupling, fre- for each surface as well as for the overall measurement quency span, etc. surface with or without “A” weighting. It is also possi- During the measurements, the program computes the ble to exclude some frequencies from the calculation sound power level for each surface and each frequency procedure selecting them directly from a list. Figure 2 complying with the Standard flowchart, and provides shows the numerical and graphical outputs for a 1/3 octave band analysis associated with the overall measurement surface represented in Figure 1. The histogram depicts, for each frequency band, the sum of both linear and “A” weighted sound power levels coming from the five measurement surfaces enveloping the source.

REFERENCES

1. F.J. Fahy, Sound Intensity, Elsevier Applied Science, London, 1989.

2. ISO 9614-1:1993, Acoustics - Determination of Sound Power Levels of Noise Sources Using Sound Intensity - Part 1: Measurement at Discrete Points. FIGURE 1. 3D representation of the measurement surface. Sound Level Meter Software Implementation with LabVIEW

J.M. Lópeza,b, M. Ruiza,b and M. Recuerob,c

aDepartamento de Sistemas Electrónicos y de Control. Universidad Politécnica de Madrid Cta. De Valencia Km 7, Madrid 28031 Spain bINSIA. Instituto Universitario de Investigación del Automóvil. Universidad Politécnica de Madrid cDepartamento de Ingeniería Mecánica y Fabricación. Universidad Politécnica de Madrid

This paper demonstrates how a sound level meter can be developed in LabVIEW with the help of a toolkit from National Instruments. An implementation in real time is also presented using Welch algorithm to avoid.

INTRODUCTION use the data acquisition board in order to avoid errors from the acquisition process. Different VIs where LabVIEW is a graphical programming language from developed to test several aspects from IEC651 and National Instruments. Its easy of use, combined with IEC804 standards[2]. These tests are presented in table high its high power and a good variety of toolsets 1.. available, have made LabVIEW become one of the most important tools in many engineering disciplines. Table 1. Sound and Vibration toolset tests developed. Nombre del test IEC references One of the available toolsets in LabVIEW is the Sound Time Weighting (F,S,I) IEC 651: 4.5, 7.2-7.5, 9.4.1, and Vibration Toolset. This toolset provides a library 9.4.3, 9.4.4 of Virtual Instruments (VIs), LabVIEW subroutines, Time Averaging IEC 804: 4.5, 6.1, 9.3.2 that implement basic operations such as fractional Rms Detector IEC 804: 7.5, 9.4.2 octave band frequency analysis, measuring Leq, dada, etc... With the help of these VIs, the design of a sound level meter (SLM) has been accomplished using The following VIs from the Sound and Vibration LabVIEW and a data acquisition board. The sound toolset were tested[3]: level meter has been tested in accordance to IEC 651 standards to verify its quality and functionality[1]. Exp avg sound level Special attention has been pay to the execution time of the different routines in order to study the possibility Equivalent Continuous Sound Level of implementing a real time sound level meter with one-third-octave band frequency analysis capability.

The following resources were used to develop these Acceptable results were obtained from these tests so it tests: was concluded that they could be used to implement a virtual sound level meter. • National Instruments high precision data acquisition board PCI-4451 with 16 bits Another important aspect related with the Sound and resolution. Vibration toolset to be analysed was execution time. Execution time of the abovementioned VIs was • Microphone model M53 from Linear X. measured using the profiler tool provided with • PC de Pentium 166 and 64Mb RAM • LabVIEW. After several trials, the average execution LabVIEW version 5.1 time of the different VIs can be estimated in the • Sound and Vibration toolset V1.0 numbers showed in table 2. TESTS Table 2. Execution time. Several tests had been developed to validate the VI Average Time (ms) quality of the algorithms provided in the Sound and Exp avg sound level 42 Vibration toolset. These tests use sinusoidal signals Equivalent Continuous Sound Level 17 synthesized with LabVIEW and therefore they do not These execution times are good enough as to VIRTUAL SOUND LEVEL METER implement a SLM in real time. A data acquisition board from National Instruments, Another important block of VIs from the Sound and mod PCI-4451, and a microphone with its preamplifier Vibration toolset are the ones related to octave and from LinearX, mod M53, were used to develop a one-third-octave band frequency analysis. These VIs virtual SLM. To cover an analysis range up to 20 kHz were tested applying a white noise synthesized in the sample frequency must be over 40 kHz. A sample LabVIEW to the IEC-Third-octave Analysis VI. From frequency of 51.200 Hz was chosen for this a quality point of view, the results obtained in this test application. After several trials, it was observed that, were acceptable. On the other hand, excessively high with a 16K samples buffer size, the acquisition could execution times (777ms average) were measured. This be accomplished in real time but the results could be made this VI not suitable for a real time not displayed. If only one block out of each four is implementation. analysed, then the complete process can be done in real time. Figure 1 shows the Virtual Sound Level Meter user interface and its code in LabVIEW.

FIGURE 1. Virtual Sound Level Meter user interface and LabVIEW code REAL TIME FREQUENCY ANALYSIS Unfortunately, from a quality point of view, this VI has a worst response in low frequencies due to the In order to include in the SLM one-third-octave band reduce number of samples available. frequency analysis capabilities in real time, a VI was specifically developed based on the Welch ACKNOWLEDGMENTS algorithm[4] show in figure 2. This VI has an execution time of 80 ms, making it possible to The authors would like to acknowledge National developed a real time implementation of the SLM Instruments Spain for all the help provided and with one-third-octave band frequency analysis Lorenzo Barba and Carlos Diaz for their capabilities. contributions. REFERENCES

1. IEC 651, Specification for Sound Level Meter, International Electrotechnical Commision.

2. IEC 804, Integrating-Averaging Sound Level Meter., International Electrotechnical Commision

3. National Instruments, Sound and Vibration Toolset Reference Manual, Agoust 1999. FIGURE 2 Welch algorithm. 4. Oppenheim, A.V., Discrete-Time Signal processing; Prentice Hall 1989 A method for the Estimation of Loudness Based on Fuzzy Theory

M. Ferri, J. Ramis, J. Alba and J.A. Martínez.

Departamento de Física Aplicada, Escuela Politécnica Superior de Gandia, Universidad Politécnica de Valencia Carretera Nazaret-Oliva sn, 46730 Gandia, Spain

In this work, we present a method for the estimation of loudness, as a combination of normalised levels (A,B,C), given in integrative sound level meters3. Usually, the acoustic signals have been pondered with one of these normalised nets depending on its sound pressure level. However, given a source with certain spectral distribution of energy, there isn’t a common criteria about which net should be applied. To correct this problem, we propose a method, based on fuzzy sets, that provides a single sound level as a combination of both three classical pondered sound levels. A comparation is shown, given a group of signals with relatively uniform spectra, of the sound levels obtained by the proposed method with the normalised loudness levels calculated by Stevens method4.

INTRODUCTION divided in 3³=27 fuzzy hyper-sets conformed by the fuzzy logic condition “and” Integrative sound level meters, do not usually perform frequency analysis of the sound signals; if LpA is A11 and LpB is A21 and LpC is A31 thus, is absolutely impossible determinate the (Fuzzy inference) loudness level of some acoustic event. Generally the ... then sound pressure level A-weighted (dBA) is accepted Lpfuz a LpA a LpB a LpC as the best approximation to evaluate loudness. k k1 k 2 k3 Anyway, different signals with the same SPL (dBA) (consequence) may have obviously very different loudness levels (Zwicker or Stevens). To solve this point, Fuzzy Prediction (Fuzzy level): As the fuzzy inferences are Logic based model1,2 -containing information about not classical logic inferences {0,1}, they have some non-linearities in frequency and level response of membership function to the truthfulness in the human hearing- has been used. interval (0,1], so each consequence is as true as its inference. Thus the predicted level is

tr Lpfuz The Model And Its Application Field Lpfuz k k trk As the normalised nets A ,B, y C, are designed to be used respectively on small, medium & high levels, being trk the truthfulness of the k-esim fuzzy we apply a weighted average of these normalised inference, calculated as follows1 levels, increasing the value of the coefficient of level tr min (LpA), (LpB) (LpC) A if the sound level is considered small, and k A1l A2 m A3n respectively, if it is medium or high. The algorithm A : “medium” A : “big” used to determinate the value of the coefficients is A11(LpA) Ai1: “small” A12(LpA) i2 A13(LpA) i3 based on Fuzzy inferences & Fuzzy sets m1 m2 m3 The Model 0 LpA 0 LpA 0 LpA Figure 1: Fuzzy sets relative to variable LpA Entry variables: LpA, LpB, LpC (Qualitative) Variables considered on Fuzzy inferences: LpA, LpB, and LpC Fuzzy sets: Three sets related to each three variable; small (Ai1), medium (Ai2), & high (Ai3) Fuzzy inferences and consequences: In the three- dimensional space, three fuzzy sets to each 1 dimension have been defined, so the whole space is A (xo ) is the membership function of the value xo of x ? to the fuzzy set A (0< A (xo ) 1) Application field: RESULTS

Fuzzy models are capable to predict situations In the next figure it is shown how fuzzy level curves similar to that which were used to configure them, so modify its shape “looking for” loudness level curves. the model is to be used for continuous and with In the three-dimensional plot it is shown the relative uniform spectra sounds. We have chosen difference between fuzzy levels and LpA, compared these, caused for the impossibility to predict exactly with the difference between loudness levels and LpA with three inputs (LpA LpB, LpC) the loudness of a for different spectra types and sound pressure levels. sound, that, in the easier case, needs a octave

LS-LA (dB) analysis of the acoustic signal (Stevens). Anyway Lfuzzy-L (dB) Weighted levels (dBA,dBB,dBC) - sound pressure levels (dB) A these are the kind of signals we usually found in 20 environmental acoustic and industrial noise. 320 signals have been selected with SPL values 10 Lfuzzy between 60 and 130 dB and slopes between –10 0 dB/oct and 10 dB/oct; comparing the Lpfuzzy with LPC -10 de Stevens loudness level (ISO 532-1975). SPL=130 dB

SPL=110 dB 5 dB -20 LPB LS SPL=130 dB SPL=110 dB -30 FITTING THE MODEL 120 LPA Spectrum type 100 -40 40 140SPL (dB) 80 The fuzzy model depends on parameters such as the 60 Spectrum type coefficients of the variables in the polynomial Figure 2. Comparing Lpfuzzy versus Loudness level functions consequence of each inference, and the shape of the fuzzy sets (that can be defined with the abscise of the slope discontinuities and the maximum The mean quadratic error in our experimental bench 2 2 value of the membership function). These parameters (320 signals) is (Lpfuz)<3’6 dB ; (LpA)>17 dB ; 2 2 will be optimised to minimise the mean quadratic (LpB)>24 dB ; (LpC)>92 dB error, considering as correct values the Stevens loudness level CONCLUSIONS N 2 Lpfuzi LSi Applying this fuzzy model, the ordinary sound level i1 meters can be used to evaluate (in first N approximation) the loudness of many different kinds The polynomial functions have been prefixed, of acoustic events (continuous and with relative limiting the model complexity, Here there is an uniform spectra), getting much better performance example of polynomial function that using any weighted sound pressure level. if LpA is “big” and LpB is “big” and LpC is “med” REFERENCES then 1) G. Cammarata, A. Fichera, S.Graziani and L. 1 1 1 Lpfuz ca LpC cb LpC cc LpB Marletta, Fuzzy logic for urban traffic noise k 3 3 3 prediction, Journal of Acoustical Society of ca cb cc 1 America 98, 1995, pp. 2607-2612 2) Y. Kato and S. Yamaguchi, A systemathical Notice that if some level is small, medium or big is study for psychological impression caused by associated respectively to LpA, LpB or LpC. fluctuating random noise based on fuzzy set There are only three set high considered: small sets theory, J. Acoust. Soc. Am. 91, 1992, pp 2748-55 high Ai1, medium sets high Ai2 and big sets high Ai3. 3) UNE-EN 60651, Sonómetros, Asociación Definitively, the model depends on thirty parameters Española de Normalización y Certificación (two abscises of six sets, four abscises of three sets, (AENOR), 1.996 three ordenades, and the additional coefficients ca, cb 4) ISO 532-1975: Method for calculating loudness and cc). Heuristic algorithms have been used: the level, International Standard Organization, 1975 gradient method, and different neural network ones.