SOUND INTENSITY PROBE CALIBRATOR FOR FIELD USE: CALCULATING THE SOUND FIELD IN THE CALIBRATOR USING BOUNDARY ELEMENT MODELLING

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1 Pge 1 of 1 SOUND INTENSITY PROBE CALIBRATOR FOR FIELD USE: CALCULATING THE SOUND FIELD IN THE CALIBRATOR USING BOUNDARY ELEMENT MODELLING PACS REFERENCE: Fm Ginn, Bernrd; Olsen,Erling; Cutnd,Vicente; Grmtorp,John; Eriksen,Anders Brüel & Kjær, Sound nd Virtion Skodsorgvej 307 DK-2850 Nærum Denmrk Tel e-mil: kginn@kdk.com ABSTRACT The newest genertion of sound intensity mesurement equipment is smll nd light enough to e hndheld when used for mesurements in the field. This increses the need for field verifiction of the equipment. Field verifiction must e esy to perform nd should not require the equipment to e tken prt. Therefore it ws decided t Brüel & Kjær to develop n intensity proe clirtor tht could e used for the two-microphone intensity proe s it is, without dismounting the spcer. The geometry of the cvity of the clirtor with proe is rther complex, nd it turned out tht simple model sed on geometric considertions could not e mde for predicting the coustic properties of the clirtor. Therefore Boundry Element Model of the clirtor cvity ws developed nd successfully used in the design of the clirtor. The clcultions re shortly descried, nd the sound fields in the coupler with different cvity geometries nd source configurtions nd the corresponding microphone responses re discussed. INTRODUCTION The newest genertion of sound intensity mesurement equipment is smll nd light enough to e hndheld when used for mesurements in the field. The hnd-held Brüel & Kjær Investigtor Sound Intensity System Type 2260E/3595 is good exmple of such mesurement equipment. As in ll mesurements, the equipment for sound intensity mesurements must e clirted nd verified efore nd fter use. While in the lortory it is not so importnt how the clirtion is mde, field clirtion nd verifiction must e esy to perform nd should not require the equipment to e tken prt. Since this is not the cse with sound intensity clirtors ville until now, it ws decided t Brüel & Kjær to develop new intensity proe clirtor for field use. The design gols for the clirtor were: i) tht it could e used for the Brüel&Kjær ½ two-microphone intensity proe s it is, without dismounting the spcer, ii) tht it should e usle for solute sensitivity clirtions s well s for pressure residul intensity index verifiction, nd iii) tht it should fulfil the requirements of Interntionl Stndrds IEC Type 1 nd IEC Clss 1. A prototype for the new clirtor ws designed sed on clssicl, sound cousticl considertions, e.g. symmetry, s smll volume s fesile round the proe. The design of the prototype ws not fr

2 Pge 2 of 2 from the design of the finl Brüel & Kjær Sound Intensity Clirtor Type 4297, ut it turned out to work in much smller frequency nd thn expected. The unexpected ehviour ws intensively discussed nd numer of modifictions of the prototype were mde. The ehviour could not e explined y mens of ny suggested geometricl, lumped prmeter or impednce considertions nd no significnt improvements were chieved with the modifictions. Therefore it ws decided to mke numericl model in order to find n explntion of the ehviour of the sound field in the coupler nd to see if there were ny possiilities of improvement. Since one of the uthors, Vicente Cutnd, t the sme time ws working with Boundry Element Modeling, BEM, of the interior of microphones, model of the coupler could e implemented fst with his softwre. GEOMETRY The clirtor consists of n xisymmetricl coupler cvity where the complete proe with spcer cn e inserted. Bsiclly, the coupler is cylindricl cvity in which the intensity proe is plced with mutul symmetry xis nd symmetry plne. In the prototype the coupler cvity ws connected to nother cvity with the sound source nd reference microphone through smll hole in the wll midwy etween the microphone diphrgms. In the finl design the sound source is prt of ring source situted in the coupler wll midwy etween the microphones nd connected to the cvity through slit. The cvity in the finl design is lso connected to nother cvity with reference microphone, ut tht is of minor importnce in this context. Coupler wll Sel etween coupler nd microphone Microphone diphrgms Spcer Figure 1. The coupler geometry defined for the clcultions, see lso figure 2. CALCULATIONS The BEM method used for the clcultions ws the direct colloction method in formultion for xisymmetric odies [1] with n improved clcultion method for ner-singulr integrtion [2]. The ctul formultion used llows for the clcultion of non-xisymmetric sound fields y using cosine expnsion of the cousticl vriles, i.e. pressure, prticle velocity nd excittion [3]. The terms in the expnsion represent sound field with n incresing numer of nodelines. The first term,, represents the xisymmetric prt of the sound field nd the following terms represent the non-xisymmetric prt of the sound field. In this cse, non-xisymmetric velocity distriution on the oundry ws used for the excittion. No losses were tken into considertion in the clcultions, nd the microphone diphrgms were ssumed to e locked. Clcultions were mde for wide vriety of dimensions nd shpes within the sic geometry of the coupler cvity. Here few of the clcultions re presented so s to demonstrte the influence of the vritions nd the importnt results. In the exmples the sound source is hlf ring source in the coupler wll t the symmetry plne of the proe spcer (in the middle of the coupler). Also, one of the microphones is slightly displced from its correct position so tht the gps etween the spcer nd the diphrgm re different t the two microphones.

3 Pge 3 of 3 Figure 2. Photogrphs of the finl clirtor. The proe is ½ proe with 12 mm spcer. The slit with the sound source is seen in the middle of the coupler cvity. x x c d x x Figure 3. Coupler with different dimeter nd with nd without spcer. Hlf-ring source. Condition numer plots for the first four terms in the cosine expnsion of the sound field. : 7.2 mm with spcer. : 8.0 mm with spcer. c: 8.5 mm with spcer. d: 8.0 mm without spcer. The condition numer of the coefficient mtrix is convenient mens to locte the eigenfrequencies of the coupler [4]. This is due to the instility generted in the system of equtions in the vicinity of such eigenmodes. Since the condition numer is mesure of the system ill-conditioning, it presents mxim t those frequencies. In figure 3 the condition numers re shown for the system of equtions for the first four terms of the cosine expnsion. Wheres the eigenfrequencies of the configurtions with the spcer do not correspond in simple wy to the dimensions of the coupler, the eigenfrequencies for the

4 Pge 4 of 4 configurtion without the spcer corresponds closely to wht must e expected for cylindricl cvity. With the spcer the frequency of the xisymmetric modes increses with incresing dimeter while the frequency of the non-xisymmetric modes decreses with incresing dimeter. The clculted sound fields in the coupler t frequencies close to the eigenfrequencies shown in figure 3 re for the modes elow 10 khz in figures 4 to 7. In the nrrow coupler the lowest eigenmode is n xisymmetric longitudinl mode. Note, tht the phse is opposite t the two microphone diphrgms. This will not e the cse if the gps t the microphones re exctly sme. However, the sound field is Figure 4. Sound field t 7.55 khz in 7.2 mm coupler with spcer nd hlf-ring source. : modulus in db, : phse in. Figure 5. Sound field t 9.38 khz in 8.0 mm coupler with spcer nd hlf-ring source. : modulus in db, : phse in. unstle t this frequency nd will chnge with ny smll chnge in the dimensions. The lowest modes of the 8.0 mm nd 8.5 mm coupler re trnsversl modes. The sound field is in opposite phse in the two sides of the coupler nd the sound pressure level is high. The 8.0 mm coupler hs longitudinl mode t slightly higher frequency. The sound field t tht frequency is comintion of trnsversl nd longitudinl wve.

5 Pge 5 of 5 Figure 6. Sound field t 9.51 khz in 8.0 mm coupler with spcer nd hlf-ring source. : modulus in db, : phse in. Figure 7. Sound field t 8.72 khz in 8.5 mm coupler with spcer nd hlf-ring source. : modulus in db, : phse in. DISCUSSION As shown ove, the sound field in the coupler with the sme excittion chnges rpidly with the coupler dimeter in wy so tht there is n optiml dimeter for the coupler cvity with the given geometry. With smll dimeter nd thus nrrow gp etween the proe nd the coupler wlls the xisymmetric modes pper t lower frequencies thn the non-xisymmetric modes. With incresing dimeter the frequencies of the xisymmetric modes increse while the frequencies for the non-xisymmetric modes decrese. The optimum dimeter is the dimeter where the modes hve the sme frequency since this gives the highest ndwidth without resonnces nd therey stle sound field. The chnges of the sound field with dimeter illustrtes why the modes of the cvity with the spcer cnnot e found with simple geometricl considertions. The cvity cnnot e divided into sustructures tht cn e identified s eing cvities, tues or trnsmission lines. Rther, ll prts of the cvity with the spcer re something in etween such cousticl elements. The process in the development project on which this pper is sed clerly shows the vlue of numericl clcultion methods. The dvntge most often mentioned in the literture is the possiility of mking mny virtul prototypes, tht is, testing mny vrints of design. However, more importnt dvntge of using the clcultions here is tht deeper understnding of the sound field in the coupler nd the prolems in the development were otined. Bsed on the clcultions descried in the previous section the coupler in the intensity proe clirtor ws designed with dimeter of 8.0 mm. In the first design of

6 Pge 6 of 6 the coupler the dimeter ws chosen to e s smll s prcticlly possile. It ws ctully discovered efore the clcultions were tken into use tht some, ut not ll, couplers with lrger dimeter hd etter performnce, ut since there were no cler explntion nd since it is not prcticlly possile to mke severl prototypes this did not led to conclusion on the design. Furthermore, even more prototypes my not hve led to the finl design since the informtion on the sound field nd therey the explntion of the differences could only hve een otined with highly complicted mesurements on mny prototypes. The microphone responses were lso considered during the development of the coupler. In principle the microphones re only sensitive to the xisymmetricl modes of the sound field nd therefore nonxisymmetric modes should not influence the performnce. Although ny rel microphone my exhiit some minor sensitivity to non-xisymmetricl modes this is proly not the only reson the coupler does not perform well when non-xisymmetric modes re present. Rther, ecuse the sound field vries so much in the coupler ner the eigenfrequencies, the xisymmetric prt of the sound pressure in the rel coupler my very well e little different t the two microphones, nd this difference would e mesured even with perfect microphones. For this reson it is not possile directly to compre the clcultions with mesurements with the proe in the coupler nd therefore such comprisons re not shown here. Wht could e seen ws tht the couplers performed well t frequencies up to round 2/3 of n octve elow the first eigenfrequency of the coupler. It should e rememered tht in this context good performnce mens less thn 0.1 db nd 0.2 difference etween the two microphones t frequencies round 5 khz. The Sound Intensity Clirtor Type 4297 tht is the result of the development project descried here is very close to the fulfillment of the design gols initilly set up for the project. Without the spcer the clirtor fulfils the requirements of IEC Clss 1. The pressure-residul intensity index of the sound field is lrger thn 24 db in 1/3 octve nds from 50 Hz to 6.3 khz. However, with the spcer the pressure-residul intensity index is slightly lower thn 24 db in the 6.3 khz 1/3 octve nd. The clirtor cn still e used for verifiction of the equipment with the spcer in dily use, ut it does not fulfil the stndrd completely. The numericl clcultions showed tht this ws the est performnce tht could e chieved for coupler where the proe could e inserted without dismounting the spcer. CONCLUSIONS In this pper it hs een demonstrted how BEM clcultions successfully led to working design of sound intensity clirtor. The sound field in the coupler could not e predicted with clssicl methods. The clcultions did not only led to successful design ut lso gve understnding of the ehviour of the sound field in the clirtor tht could not e otined without the clcultions. The clcultions descried in this pper led development project from filure into success. Numericl clcultions re certin to e developed nd used in future cousticl design projects t Brüel & Kjær. ACKNOWLEDGEMENTS The uthors wish to thnk Peter Møller Juhl t Odense University in Denmrk for his contriutions to the work with the clcultions descried here. The uthors lso wish to thnk Erling Frederiksen t Brüel nd Kjær nd Finn Jcosen t the Technicl University of Denmrk for vlule discussions during the development of the intensity clirtor. REFERENCES [1] A.F.Seyert, B.Soenrko, F.J.Rizzo, D.J.Shippy, "A specil integrl eqution formultion for coustic rdition nd scttering for xisymmetric odiues nd oundry conditions", J.Acoust.Soc.Am., 80, (1986) [2] V.Cutnd, P.M.Juhl, F.Jcosen, "On the modeling of nrrow gps using the stndrd oundry element method ", J.Acoust.Soc.Am., 109, (2001) [3] P.M.Juhl, "An xisymmetric integrl eqution formultion for free spce non-xisymmetric rdition nd scttering of known incident wve", J.Sound Vi., 163, (1993) [4] M.R. Bi, "Study of coustic resonnce in enclosures using eigennlysis sed on oundry element methods", J.Acoust.Soc.Am., 91, (1992)