The Sound Power as aReference forSound Strength (G...

ACTA ACUSTICA UNITED WITH ACUSTICAVol 101 (2015) 892 ndash 907

DOI 103813AAA918884

The Sound Power as a Reference for SoundStrength (G) Speech Level (L) and Support (ST )Uncertainty of Laboratory and In-Situ Calibration

R H C Wenmaekers C C J M HakDepartment of the Built Environment unit BPS Laboratorium voor Akoestiek Eindhoven Universityof Technology PO Box 513 5600 MB Eindhoven The Netherlands rhcwenmaekerstuenl

SummarySome room acoustic parameters require the sound power of the sound source The Sound StrengthG uses the freefield sound pressure level at 10 meters distance as a reference value Speech intelligibility parameters like the A-weighted Speech Level LpAS4m and the Speech Transmission Index STI can require an absolute source leveldefined at 1m distance from the sound source The Early and Late Support parameters use the sound level at 1mdistance as a reference level In this paper all proposed methods to obtain the sound power level for room acousticapplications are investigated using various omnidirectional sound sources with a dodecahedron shape containing12 loudspeakers It is shown that for octave bands 250 to 8000Hz the sound power can be determined with08 dB uncertainty when using precision methods (diffuse field intensity or free field) Alternative laboratorycalibration methods that only measure in a single plane of the sound source show deviations up to 2 dB peroctave band Different stepwise rotational averages used in such a single plane free field method have beeninvestigated It can be concluded that the uncertainty is significantly reduced only when using 125 degree steps(ISO 3382-1) and when using equal-angular rotations with 5 or 7 steps Furthermore the uncertainty of in-situ calibration has been investigated A comparison of results from different researchers shows that a correctionfactor should be applied to correct the in-situ calibration for its deviation from the laboratory calibration For eachcalibration method the uncertainty is presented Results show that some methods might be sufficiently accurateto be able to measure single number ratings for G ST LpAS4m and STI with an uncertainty in the order ofmagnitude of 1 JND provided that no other measurement errors are introduced in the measurement chainPACS no 4355Br 4355Mc 4358Vb 4358Fm

1 Introduction

Various room acoustic parameters have been introducedsome of which have been included in the ISO standard3382 on the measurement of room acoustic parameters [1]Many room acoustic parameters are defined in such a waythat the sound power of the sound source is not relevantEnergy decay related parameters (EDT T20 and T30) en-ergy related parameters (C80D50 Ts) lateral energy mea-sures (JLF JLFC ) spatial impression parameters (IACC)and the spatial decay parameter (D2S ) all make use of arelative definition

However some room acoustic parameters do requireknowledge of the sound power of the sound source Levelparameters (G LJ and LpAS4m) and stage support pa-rameters (STearly and ST late) measure the amount of en-ergy of a room impulse response within a certain time in-terval andor direction and compare it to the energy ofthe impulse response from the same sound source mea-

Received 07 July 2014accepted 05 August 2015

sured in the free field at a certain distance Also whendetermining speech intelligibility parameters like STI thesignal to noise ratio is determined based on a ratio of ab-solute sound pressures (following ISO 16268-16 [2] onlyif background noise is taken into account and followingISO 3382-3 [3] for all measurements in open plan offices)Following ISO 3382 all of these room acoustic parame-ters should be determined using an omnidirectional soundsource A certain deviation from omnidirectionality is al-lowed and the deviation limits are given in the standardLundeby et al [4] asked 8 different teams to determine

room acoustic parameters for 10 sourcendashreceiver combi-nations in a 1800m3 auditorium He found a standard de-viation for the level parameter Sound Strength G of only02 to 03 dB for the octave bands 125 1000 and 4000HzThese results would suggest that G can be measured withvery high accuracy even when using a variety of loud-speaker types (a single loudspeaker in a box a cube withsix loudspeakers and a dodecahedron with twelve loud-speakers) Unfortunately in their paper it is not explainedhow the sound sources were calibrated In theory the re-lation between the sound power of a point source and itssound pressure level (SPL) in the free field is clear How-

892 copy S Hirzel Verlag middot EAA

Wenmaekers Hak Sound power calibration for reference ACTA ACUSTICA UNITED WITH ACUSTICAVol 101 (2015)

ever in earlier research we have shown that different meth-ods to obtain the free field SPL may yield different resultswith deviations more than 2 dB for individual octave bands[5] The low standard deviations found by Lundeby et al[4] between 8 different measurement teams are thereforehighly questionableThe deviations in sound power determination are prob-

lematic as one would like to measure most room acous-tic parameters within the limits of their Just NoticeableDifference (JND) which can be as low as 1 dB for somelevel parameters It is necessary to find out when measure-ment methods are sufficiently accurate and which methodsshould be avoided In this paper the difference betweenvarious calibration methods and the impact of simplifica-tions within these methods are investigated This is doneby using available data from literature and to close someknowledge gaps or to check whether the findings from lit-erature can be reproduced by performing additional mea-surements or analysing shared data from other researchersIn some cases results are only available from one sin-gle research(er) using one single loudspeaker type whichis often dodecahedrally shaped We did not perform suchextensive amount of measurements necessary to signifi-cantly identify all uncertainty contributions in each mea-surement method but the main conclusions are based onresults from multiple investigations involving various re-searchers and sound sources The overview presented inthis paper provides valuable insight in the merits of soundsource calibration for room acoustic purposes and somemajor problems have been identifiedIn this paper the background on the most relevant room

acoustic parameters and common calibration methods isdiscussed in Section 2 In Section 3 the differences ofvarious laboratory measurement methods concerning thesound power as a reference for room acoustic parametersare discussed Findings from literature and new researchhave been combined to investigate uncertainties In Sec-tion 4 problems with the directivity of the sound sourceare discussed which is particularly important for the cali-bration methods that only measure in the horizontal planeof the sound source while taking rotational averages InSection 5 in-situ measurement methods are discussed in-cluding (floor) interference effects and variations over dif-ferent positions In Section 6 the paper will conclude witha summary and conclusions on the uncertainty that can beexpected from using the available methods

2 Background

21 Room acoustic parameters and sound power

The sound strength G is used to investigate the sound dis-tribution in a concert hall or to compare the sound levelsbetween different concert halls Originally Lehmann in-troduced the Staumlrkemass or lsquoStrenght Indexrsquo which wasdefined as the difference in SPL in the hall caused by anomnidirectional sound source on the stage and the soundpower level Lw of the same sound source [6] Later on Gwas defined as the SPL at a listener position in the hall

with reference to the SPL at 10m distance from the samesound source in a free field The late lateral sound energylevel LJ is similar to G in its definition of the referencelevel Here the late sound energy arriving after 80ms at afigure-of-eight microphone is compared to the total soundenergy at 10m distance at an omnidirectional microphonein the free field For G the 10 meter distance was chosenby Barron and Lee for reasons of convenience because thischoice will often result in measured values of the soundlevel Lp close to the reference value Lp10m and hence val-ues of G close to 0 dB [7] G can either be determined us-ing stationary noise or using impulse responses [1] wherethe sound pressure exposure levelLpE is determined (up tothe time point that the energy decay or Impulse to NoiseRatio (INR) [8] is 30 dB or lower) The single numberrating for G is calculated from the average of the 500 and1000Hz octave band defined by ISO 3382-1 as GM andthe Just Noticeable Difference (JND) is 1 dB For LJ thesingle number rating is calculated from the average of the125 to 1000Hz octave band denoted by LJavg The JNDfor LJ is unknown

LpAS4m is the A-weighted SPL of normal speech at4 meter distance from an omnidirectional sound sourceLpAS4m is used together with D2S the decay of soundper doubling of the distance to describe the decay ofspeech sound in an open plan office A standardised spec-tral level LpS1m(f ) defined at 1 meter distance is usedto describe the sound power of the normal speaker [3]After A-weighting the speech spectrum the sound levelin dB(A) is predominantly dependent on the level in the500 and 1000Hz octave bands The distance of 4m is cho-sen as a nominal distance where the far field starts [9]In a similar way the absolute SPL of speech is used inthe calculation of the Speech Transmission Index (STI)where the SPL of the received speech LpS(f ) and the SPLdue to background noise LeqN (f ) is used to determinethe signal to noise ratio (SNR) In both LpAS4m and STIparameters the sound power of the sound source mustbe known to be able to apply the standardised spectrumand level The JND for the STI is 003 [10] The impactof reverberation on STI is small in open plan offices asshown by Wenmaekers et al [11] In a worst case sce-nario where reverberation does not affect the STI calcula-tion and the influence of background noise is fully domi-nant we can translate the JND of the STI as a JND of theSNR in dB In this way the maximum possible error inSignal level (or speech level LpS ) due to calibration un-certainty can be investigated In this paper the individualerrorsΔLpS(f ) in dB over the octave bands 125 to 8000Hzare translated into a modulation transfer index MTI(f ) by(ΔLpS(f )+15)30 The MTI(f ) is weighted in accordancewith IEC 60268-16 and the STI is calculated Then to ar-rive at a weighted single-number rating errorΔLpSsingle iscalculated as (STItimes30)minus15 dB A difference of 003 in STIappears at approximately 1 dB difference in ΔLpS single

The stage acoustic parameters Early Support STearlyand Late Support ST late are used to investigate the ensem-ble conditions and perceived reverberance by musicians on

893

ACTA ACUSTICA UNITED WITH ACUSTICA Wenmaekers Hak Sound power calibration for referenceVol 101 (2015)

Table I Overview of room acoustic quantities that depend on a reference level because the 500ndash1000Hz bands are dominant afterA-weighting the speech spectrum the 500 and 1000Hz bands average level will be used an indicator for LpAS4m estimated byAC Gade

Acoustic Quantity Parameter Reference JND Single Number

Sound Strength G Lp10m or LpE10m 1 dB 500ndash1000Hz

Late Lateral Sound Energy Level LJ Lp10m or LpE10m not known 125ndash1000Hz

A-weighted speech level at 4m LpAS4m Lw or Lp1m not known A-weighted level

Speech Transmission Index STI Lw or Lp1m 003 STI Weighted over(= 1 dB in ΔLpSsingle) 125ndash8000Hz

Early Support STearly or STearlyd Lp1m or LpE1m 2 dB 250ndash2000Hz

Late Support ST late or ST lated Lp1m or LpE1m 2 dB 250ndash2000Hz

concert hall stages Both parameters are commonly deter-mined at 1 meter distance from an omnidirectional soundsource and measure the early or late reflected sound en-ergy relative to the direct sound energy of the sound source[12 13] More recently the extended parameters STearlyd

and ST lated have been introduced that can be used to studythe transfer of reflected sound energy over the stage atvarious distances [14] The 1 meter distance reference ischosen as it is comparable to the distance of the musicalinstrument to the playersrsquo ears [12] (even though other re-searchers suggested that this distance is smaller in manycases [15 16]) The direct SPL at 1m distance was in-tended to be the free field sound level as explained byGade [17] The method described in ISO 3382 uses a ref-erence level measured in-situ The single number rating forthe ST parameters is the average of the four octave bands250 to 2000Hz and the estimated JND for the ST parame-ters is 2 dB [18]

An overview of the parameters mentioned in this para-graph is presented in Table I The different frequencyranges are used in the different parameters because theyrelate to different perceptual aspects In this paper the fre-quency ranges as suggested by ISO 3382 are used

22 Calibration methods in room acoustics

A large number of methods for the determination of soundpower levels of sound sources is described in the ISO 3740series [19] ranging from reverberation room methods tointensity or pressure level measurements in a (hemi) freefield Depending on the desired accuracy different meth-ods can be applied For the determination of the soundpower level of an omnidirectional sound source used forroom acoustic measurements ISO 3382-1 suggests twodifferent calibration methods ISO 3382-3 refers to thissame part of the standard and suggests determining thesound power with at least lsquoengineering accuracyrsquo

Following the first method mentioned in ISO 3382-1one directly measures the SPL at 10 meters distance tothe sound source in an anechoic room or in case only asmaller anechoic room is available one measures at a dis-tance of at least 3m (to avoid being in the near field ofthe loudspeaker) and translates the measured SPL to a 10

Figure 1 Side view of vertical rotation axis and horizontal mea-surement plane of a dodecahedron loudspeaker used in the lsquosin-gle plane free field methodrsquo for calibrating omnidirectional soundsources

meter distance In accordance with ISO 3382-1 the en-ergy mean sound level needs to be determined from 29measurements at every 125 step rotation of the soundsource It is remarkable that the sound power of the om-nidirectional sound source which most often has a dodec-ahedral shape containing 12 loudspeakers is determinedfrom measurements in one single horizontal plane onlysee Figure 1 In contrast the methods in the ISO 3740 se-ries suggest measuring over an equally spaced grid aroundthe sound source In ISO 3382-1 no scientific study isquoted that motivates the 125 rotation method nor is itsaccuracy discussed Among others this method has beenapplied by Barron and Lee [7] Aretz and Orlowski [20]and Dammerud [21] In this paper this method will be de-noted the lsquosingle plane free field methodrsquoThe second method described in ISO 3382-1 uses the

precision method for reverberation rooms in accordancewith ISO 3741 [22] When using stationary noise thesound power is determined following the full standardrsquosprocedure When using impulse responses a system cali-bration can be performed in the reverberation room with-out measuring the actual sound power During a systemcalibration the sound exposure level LpE is measured inthe reverberation room then corrected for the amount of

894


Table II Overview of calibration methods using for room acoustic parameters

Calibration method Standard Procedure Averaging

1 Single plane free fieldmethod (ISO 3382-1 AnnexA)

none SPL measured in an anechoic room atany distance gt 3m and translated to theSPL at 10m distance

Average taken from 29 rotations in thehorizontal plane with steps of 125

2 Reverberation Room (ISO3382-1 Annex A)

ISO 3471 SPL and T measured in a reverberationroom of at least 200m3 for octave bandsge 125Hz

SPL measured over 30 seconds for 6microphone positions (if standard devi-ation is below 15 dB)

3A In-situ on stage original(ISO 3382-1 Annex C)

none The direct SPLSEL measured in-situfrom the measured impulse responseusing a 0ndash10ms window at 1m source-receiver distance

Single measurement at random anglerelative to the omnidirectional soundsource

3B In-situ on stage update[17]

ISO 3471 idem 3A with additional correction for1m distance SPL derived from a soundpower measurement in a reverberationroom

Single measurement at fixed angle rela-tive to the omnidirectional sound source

3C In-situ on stage by others[24 25]

none The direct SPLSEL measured in-situfrom the measured impulse responseusing a 0ndash35 or 0ndash5ms window at 1msource-receiver distance

Single measurement at random fixedangle relative to the omnidirectionalsound source

absorption in the room and used as a reference for any fu-ture sound exposure level measurements (comparing rela-tive levels) According to ISO 37411999 in octave bandsthe uncertainty in terms of the standard deviation of re-producibility is equal to or less than 25 dB for 125Hz15 dB for 250Hz 1 dB from 500Hz to 4000Hz and 2 dBfor 8000Hz (in the 2010 edition of ISO 3741 the octaveband values are no longer mentioned) Among others thismethod has been applied by Gade [23] Virjonen et al [9]and Beranek [24]

Essentially the Support parameters STearly and ST late

as described in ISO 3382-1 use a third method to deter-mine the sound power level of the sound source A refer-ence level is determined in-situ from the impulse responsemeasured at 1m distance using a 0-10ms window Withinthis 0-10ms time interval the floor reflection is includedwhich introduces an error in the determination of the directsound Also errors due to loudspeaker directivity are be-ing introduced because of the use of only one single mea-surement Gade [17] suggests to compensate for these er-rors by first determining the SPL at 1 meter distance basedon a sound power laboratory measurement After that themeasured SPL at 1 meter distance is determined in-situ ona reflective surface and for a certain fixed angle or aimingpoint relative to the omnidirectional sound source The dif-ference between these two values could be applied to theSTearly and ST late as a fixed correction factor for future in-situ measurements After performing this procedure oncethere would no longer be the need for calibrating the soundsource in the laboratory (in the short term) It should benoted that this correction procedure is not mentioned inISO 3382-1Similar in-situ methods have been used by various re-

searchers to measure G Beranek [24] notes that all re-searchers mentioned in his paper used an in-situ calibra-

tion measuring the sound pressure level at 1 meter dis-tance except for the Takenaka RampD institute who useda reverberation room calibration Dammerud and Barron[25] used a reference microphone at 1 meter during theirscale model measurements as the used spark source couldnot reproduce the same output power for every measure-ment They extracted the direct sound by windowing overthe 0 to 35ms interval of the impulse response San Mar-tin et al [26] used a similar approach on concert hall stagesby windowing over the 0 to 5ms interval An overview ofall mentioned calibration methods is presented in Table II

23 Signal processing in-situ measurements

In case of source and receiver heights of 10 m the floor re-flection will arrive 36ms after the direct sound and for the250Hz octave band which is the most critical in the 250ndash2000Hz frequency range these two components will besmeared out over the whole time interval 0ndash10ms due tothe band filtering So it seems to be impossible to separatethe direct sound and floor reflection by windowing Actu-ally earlier research by the authors [14] has shown that toreduce the error in determining the sound level of the directsound separately from a signal with direct sound and a sin-gle equally loud reflection to le 01 le 05 and le 10 dBa minimum distance between direct sound and reflectionof 17 12 and 9ms is required respectively for the sepa-rate octave bands 250 500 1000 and 2000Hz (see An-nex for the type of signal processing used) When measur-ing sound levels it is also necessary to take into accountthe size of the wavelength and it is recommended to usea time window of at least one corresponding wavelengthFor the 250Hz octave band with lower edge frequency at176Hz this suggests that the time window should at leastbe 6ms and for the 125Hz octave band with lower edgefrequency at 88Hz at least 11ms So it seems that a min-

895


imum time window of 11ms is needed for highly accuratemeasurements starting from the 125Hz octave band whileroom reflections should not arrive before 17ms This againshows that the floor reflection cannot be excluded

Other elements of signal processing exist that mightcause variation of results from different researchersAmong others the determination of the impulse responsestarting point can be done in various ways which mightinfluence results from in-situ calibrations Also as pointedout by Lundeby et al the method of filtering can be of in-fluence on results of level calculations Uncertainty intro-duced by signal processing is mostly relevant for judgingreproducibility and less relevant for judging repeatabilityIn our paper we assume that the uncertainty contributionof the signal processing is part of the whole measurementprocedure and is therefore included in the analysis De-tailed analysis of uncertainty due to signal processing isoutside the scope of our paper but would be interestingfor further research

3 Laboratory calibration measurements

31 Precision methodsThe uncertainties in the determination of the sound power(or reference SPL) of sound sources have been studied un-der laboratory conditions by Vorlaumlnder and Raabe [27]They organised a round robin among 8 laboratories duringwhich the sound power of a BampK 4204 reference soundsource was measured in hemi-anechoic and in reverber-ant conditions The uncertainty due to the use of differenttypes of signal processing was included in the researchThey concluded that in general both methods yield al-most exactly the same results except in the frequencyranges below 100Hz and above 10 kHz The maximumstandard deviation σ and reproducibility limit R (proba-bility level of 95 using a coverage factor of 28) of bothmethods are 10 dB and 28 dB in the 125Hz octave bandand 03 dB and 08 dB in the 250 to 8000Hz octave bandsThe reproducibility is similar to the values suggested byISO 37411999To the knowledge of the authors no literature exists

about the stability of dodecahedron loudspeakers whichis known to be a critical design element for the type ofsound sources Sound power measurements (at 120 dBsound power level) performed by the authors in a 90m3 re-verberation room repeated 10 times over four years usinga dodecahedron loudspeaker BampK 4292 a BampK 2734 am-plifier and a BampK 4189 microphone on a rotating boomshowed a standard deviation of 03 dB in the separate 250to 8000Hz octave bands (the 125Hz octave band couldnot be evaluated as the room volume was too small) Thestandard deviation of our measurement with the dodeca-hedron sound source is similar to the standard deviationfound by Vorlaumlnder and Raabe for the reference soundsource It shows that even over a four year period the sta-bility of a dodecahedron loudspeaker in this case a BampK4292 can be as high as a reference sound source type BampK4204 provided all other used measurement equipment ishighly stable too

(a)

(b)

(c)

Figure 2 (a) Measurement setup in the reverberation room (usinga reference source) (b) Measurement setup in the anechoic roomusing the intensity probe (a metal grid was used to define thescanning surface) (c) Measurement setup in the anechoic roomusing a omnidirectional microphone and a turntable (single planefree field method)

Furthermore the difference between two types of pre-cision calibrations has been investigated for the dodecahe-dron loudspeaker type BampK 4292 to investigate whetherthe difference would fall within the reproducibility limitsas found by Vorlaumlnder and Raabe and mentioned in ISO37411999 The sound power was determined in a 200m3

reverberation room in accordance with ISO 3741 see Fig-ure 2a and in an anechoic room via a sound intensity mea-

896


surement using a sweep scan method following ISO 9614-3 [28] see Figure 2b (see Annex for details) Note thatthe intensity measurement used by us is different from thesound level measurement used by Vorlaumlnder and Raabe al-though both are executed in a (hemi)anechoic room Ourmeasured results for the direct reverberation method andanechoic intensity method are presented in Figure 3a asaverage sound power levels relative to the average resultof both measurement methods The maximum differencebetween Lw for the methods individually and their aver-age Lw is at most 03 dB over the 250ndash4000Hz octavebands with a standard deviation of 05 dB over the individ-ual receiver positions or scanning surfaces In the 125 and8000Hz octave bands the maximum difference is largerup to plusmn10 dB with a standard deviation up to 10 dB Forthe 125ndash4000Hz octave bands the difference in our re-sults are well within the reproducibility limits of R =08 dB at 250ndash8000Hz andR = 28 dB at 125Hz as foundby Vorlaumlnder and Raabe We can conclude that the differ-ence in results from our two different measurements canbe attributed to each test methodsrsquo precision

32 Full sphere versus single plane

Besides the reverberation room precision method ISO3382-1 recommends performing a sound power measure-ment in an anechoic room where the average level is de-termined from 125 rotation of the sound source denotedhere by the lsquosingle plane free field methodrsquo Unlike theintensity measurement where a full sphere around thesource is measured in the ISO 3382-1 method only thehorizontal plane is measured (see Figure 1) To find outif an error is introduced by measuring in a single planeinstead of measuring around a full sphere we performedmeasurements using the single plane free field method at1m and 7m distance from the physical centre of the om-nidirectional dodecahedron sound source in an anechoicroom We compared the results to the intensity measure-ment presented earlier which takes into account all di-rections A noise signal was recorded at both distancessimultaneously while rotating the sound source using aturntable see Figure 2c (see Annex for details) The devi-ation in measured sound power at both distances from theresults of the intensity measurement is presented in Fig-ure 3b It is shown that the results for the two measureddistances follow a similar trend The average over all oc-tave bands is equal for both distances The deviation of theresults using the single plane free field method from theresults from the intensity measurement is above 05 dB upto 21 dB for almost all octave bands see figure 3b Sur-prisingly for the frequency range below 500Hz where thedodecahedron sound source is expected to be fully omnidi-rectional the deviation is 08 dB on average Note that theexpected reproducibility for precision calibration methodsis 08 dB for 250 and 500Hz This means that the devi-ation up to 500Hz that we found comparing the inten-sity method and the single plane free field method canbe attributed to the overall precision of the measurementmethod However the larger deviation above 500Hz might

ΔLw[dB]

-20

-15

-10

-05

00

05

10

15

20

125 250 500 1000 2000 4000 8000

ΔLw[dB]

IntensityHorizontal plane 1mHorizontal plane 7m

(a)

(b)

(c)

ΔLw[dB]

ΔLw[dB]

Frequency [Hz]

(d)

-20

-15

-10

-05

00

05

10

15

20

125 250 500 1000 2000 4000 8000

Diffuse

Intensity

-20

-15

-10

-05

00

05

10

15

20

125 250 500 1000 2000 4000 8000

ITA1ITA2ITA3ITA5ITA6

-20

-15

-10

-05

00

05

10

15

20

125 250 500 1000 2000 4000 8000

ITA4

ITA7

ITA8

Figure 3 (a) Comparison of the sound power levels measuredin diffuse field using a omnidirectional microphone and ane-choic conditions using an intensity probe relative to the mean(b) Comparison of the sound power level measured at 1m and7m distance in the horizontal plane in an anechoic room rela-tive to the sound power level measured using an intensity probeover the full sphere in an anechoic room (c) The deviation be-tween the full sphere average and single plane average for var-ious moderate size dodecahedron loudspeakers (with a sectionof 300-400mm) (d) The deviation between the full sphere aver-age and single plane average for various small size dodecahedronloudspeakers (section approximately 100mm) that are used in athree way loudspeaker setup

897


Table III Uncertainty factors and calculated uncertainty for the precision method and single plane free field method under theassumption that the deviation in different octave bands is correlated estimated by the average over the octave bands offset anddeviation at 95 confidence level and 28 coverage factor ll lower limit ul upper limit

Octave band with mid frequencies [Hz] Single number ratings average125 250 500 1000 2000 4000 8000 125ndash1000 250ndash2000 500ndash1000 STI

σprecision 1 03 03 03 03 03 03 05 03 03 04offsetplane 0 0 0 02 -09 -11 08 0 -02 01 -03σplane 01 01 01 02 06 05 04 01 01 01 01U95precision plusmn28 plusmn08 plusmn08 plusmn08 plusmn08 plusmn08 plusmn08 plusmn14 plusmn08 plusmn08 plusmn11U95plane 0 0 0 02 -09 -11 08 0 -02 01 -03

plusmn28 plusmn09 plusmn09 plusmn1 plusmn19 plusmn16 plusmn14 plusmn14 plusmn09 plusmn09 plusmn12U95plane ll -28 -09 -09 -08 -28 -27 -06 -14 -11 -08 -15U95plane ul 28 09 09 12 10 05 22 14 07 10 09

be caused by the simplification of measuring only a singleplane instead of measuring a full sphereTo investigate whether the high frequency deviation be-

tween the full sphere and single plane measurement foundfor the BampK 4292 presented in Figure 3b is represen-tative for dodecahedron loudspeakers in general directiv-ity data for various dodecahedron loudspeakers have beenanalysed which were measured by the Institut fuumlr Technis-che Akustik (ITA) RWTH Aachen (sources denoted ITA1to ITA4 are described in [29]) The directivity was mea-sured with a 5 degree grid over half the sphere using asimilar setup as described in Leishmann et al [30] SectionII The emitted sound power averaged over the full sphereis determined by weighting over the surface area per gridpoint as described in Leishmann et al [30] Section IV-Bequations 3 to 6 The emitted sound power averaged overa single plane was derived from the 72 measurements inthe horizontal plane in the base of the half sphere Thecalculated deviations between the full sphere average andsingle plane average are presented in Figure 3c for variousmoderate size dodecahedron loudspeakers (with a diam-eter of 300-450mm) and in Figure 3d for various smallsize dodecahedron loudspeakers (diameter approximately100mm) that are used in a three way loudspeaker setup forthe 2 kHz octave band and higher For the moderate sizedodecahedrons a similar frequency trend is found as pre-sented in Figure 3b Now we can conclude that the singleplane method introduces a systematic error with a slightvariation over different sound sources with similar size

33 Discussion on laboratory calibration measure-ments

The uncertainty of the precision calibration methods todetermine the sound power of a highly stable omnidirec-tional sound source is within 08 dB for the octave bands250ndash8000Hz However in the 125 octave band the devia-tion is found to begt 10 dB which is larger than the JND incase ofG The absolute deviation between a full sphere av-erage (any precision method) and the single plane average(as suggested by ISO 3382-1) is significant for frequencybands 2000ndash8000Hz with errors up to 21 dB for variousmeasured dodecahedron loudspeakers This systematic de-

viation can be attributed to the geometrical simplificationin the measurement methodTo determine the total uncertainty for each method

models are defined that show how the different identifiedsources of uncertainty propagate through the measurementprocedure Because the number of number of data pointsin the Vorlaumlnder and Raabe study and our studies are lim-ited it is not possible to determine its distribution How-ever following Vorlaumlnder and Raabe we have no reason todoubt whether data would not be normally distributed Thestandard deviation is expanded with a coverage factor of 2multiplied by a factor

radic2 recommended for cases with a

small amount of data This way we can expect to arrive ata level of confidence of approximately 95

The uncertainty of the precision method and singleplane free field method can be expressed by

U95precision = plusmn28 σ2precision (1)

and

U95plane = offsetplane plusmn 28 σ2plane + σ2

precision (2)

where U95precision is the uncertainty of the precisionmethod at 95 confidence level in dB (coverage factor28) σprecision is the maximum standard deviation of theprecision methods in dB taken from Vorlaumlnder and Raabe[27] U95plane is the uncertainty of the single plane freefield method at 95 confidence level in dB and offsetplaneand σplane is the average systematic error and standard de-viation due to geometrical simplification for 6 moderatesize dodecahedron loudspeakers in dB

Table III shows the values for the parameters usedin Equation (1) and (2) and the calculated uncertaintyU95precision for the precision method and U95plane forthe single plane free field method It seems that for theroom acoustic parameters mentioned in Section 2 and pre-sented in Table I determining all separate octave band val-ues within an JND limit of 1 dB (uncertainty at 95 confi-dence level) is not possible when using either the precisionmethods or the single plane free field method for calibra-tion For the single number ratingsGLpAS4m STearly andST late a calibration can be performed with an uncertainty

898


le 1 JND using either a precision calibration method or thesingle plane free field method For STI the uncertainty isslightly larger than the JND

4 Uncertainties due to directivity

In the previous section some directivity characteristics ofthe dodecahedron sound source were already revealed inthe difference between a sound power measurement aver-aged over the full sphere and averaged over a rotation ina single plane only In this section the impact of soundsource directivity on room acoustical measurements andsound source calibration in particular is investigated

41 Background on polyhedron loudspeakers anddirectivity

Recently the properties of omnidirectional sound sourceshave been investigated in more depth Leishmann et al[30] compared the directivities of various regular poly-hedron loudspeakers (RPL) They conclude that noneof the investigated RPLrsquos are being consistently excep-tional in omnidirectional behaviour above their lsquocut-offfrequencyrsquo the frequency above which the directivity in-creases rapidly (see [30] for the definition of lsquocut-off fre-quencyrsquo) Among others the reduction in omnidirectionalbehaviour is caused by the spread of the individual loud-speakers relative to the wavelength and by the break upphenomenon on the individual loudspeakersrsquo cone Thetetrahedron with four loudspeakers showed the best per-formance in the 4 kHz band The dodecahedron was alsofound to be a good choice among other things due to itshighest cut-off frequency (1463Hz for a 146 cm radius)and the most uniform radiation in the 2 kHz octave bandAn advantage of the dodecahedron shape is that the in-crease of the number of loudspeakers will result in a higher(possible) sound power It is striking that the icosahedronshape with 20 loudspeakers the type that was used byGade [23] did not show a more uniform radiation thanany other RPL with a lower amount of loudspeakersLundeby et al [4] raised the problem of the effect of the

directivity of the dodecahedron and the cube loudspeakeron measured room acoustic parameters They indicate thatfor 18 rotation steps of 20 a standard deviation of almost04 dB in G can be found at the 4 kHz octave band Actu-ally San Martiacuten et al [31] found that for single measure-ments in a concert hall at 18 meter distance deviationsin all room acoustic parameters except T30 were abovethe JND for random orientations of two different soundsources at octave bands with mid-frequencies above 1 kHzAlso for 24 measurements taken in the horizontal plane(see Figure 1) over a 120 area in steps of 5 using bothsound sources the standard deviation at 2 and 4 kHz islarger than one JND for G San Martiacuten et al conclude thatthe uncertainty is not sufficiently reduced when an averagevalue is taken over 3 rotations as suggested by ISO 3382-1 for field measurements (mentioned authors state that it iscommon practice to average within a 120 area in steps of40) As mentioned before for sound source calibrationISO 3382-1 recommends using 29 steps of 125

The possibility of averaging over multiple rotations withequally sized steps (for instance 4 steps of 90 degrees or6 steps of 30 degrees) has been investigated by the au-thors and our first results were presented in [32] Themaximum sound level deviation from the sound level de-termined from a full rotation average was determined forvarious equal-angular step averages For every possiblesingle rotation (= 1 step) and for every possible multiplerotation averages over equal-angular steps up to a num-ber of 8 steps with any random initial aiming point themaximum deviation in sound level from the full rotationaverage was determined at various source-to-receiver dis-tances in a concert hall An even distribution of the stepsover the full rotation was chosen to take into account smalldifferences in sound power by the different loudspeakers(instead of rotating within a single 120 area) It was con-cluded that when choosing any of the 1 2 3 4 or 6 equal-angular rotation averages the maximum deviation was notsignificantly reduced Surprisingly when using an aver-age over 5 7 or 8 equal-angular rotations the maximumpossible deviation from the full rotation average could bedramatically reduced far below the JND up to the 4 kHzoctave band for all source-to-receiver distances The do-decahedron loudspeaker has rings of 3 or 6 loudspeakersdistributed along the axis of rotation Possibly the num-ber of 5 and 7 equal-angular rotations both work becausethese are prime numbers resulting in a non-symmetricaldistribution of measurement points (These results are onlybased on one condition a random concert hall To confirmthe validity of the equal-angular averaging method underdifferent conditions similar results will also be presentedin the end of this section for anechoic conditions usingmultiple sources)Investigations were continued by Martelotta [33] who

looked at the possibilities of finding an optimal choice of(relatively small) angles for a two or three step rotationaverage with any random starting point For his study hemeasured room impulse responses for every 5 step over120 similar to San Martiacuten et al [31] He concludes thattwo measurements spaced by 60 or three measurementsspaced by 30 similarly result in the lowest standard devi-ation from the average compared to single measurements(using any of the discrete 5 steps as the initial aimingpoint) in room acoustical parametersG C50LF and EDT For a G measurement at 10 meter distance in a 1200m3

auditorium the standard deviation averaged over 2 and4 kHz was reduced from 067 dB for a single measurementto 025 dB and 031 dB for the two or three step rotationaverage

42 Comparison study of single plane rotationalaveraging methods

Table IV gives an overview of findings on deviations dueto directivity and source rotation It can be concludedthat for judging level related parameters in separate oc-tave bands ge 2 kHz and at a single position in a hall thestandard deviation due to source directivity can be largerthan the JND An even larger uncertainty can be expected

899


Table IV Overview of findings on directivity and source rotation

Authors Orientation and averag-ing

Conclusions Distance Denoted

Lundeby et al [4] 18 rotation steps of 20 σ of almost 04 dB at 4 kHz auditoriumdistance not stated

-

San Martiacuten et al [31] 2 sources with randomorientation

absolute deviation in all roomacoustic parameters (except T30)above the JND for bands gt 1 kHz

concert hall at18m distance

-

San Martiacuten et al [31] 24 single measure-ments over an 120

area in steps of 5

σ over rotation results at 2 and4 kHz above JND


lsquosinglersquo

San Martiacuten et al [31] 3 rotation averagewithin a 120 areain steps of 40

σ not significantly reduced concert hall at18m distance

lsquo0-40-80rsquo

ISO 3382-1 [1] 29 rotation averagein steps of 125

deviation unknown gt 3m in anechoicroom

lsquo29x125rsquo

Hak et al [32] 2 to 8 equal-angularrotation average

maximum deviation reducedfar below the JND for all octavebands by averaging over 5 7 or 8equal-angular rotations

concert hall at 1 5and 18m distance

lsquo2EArsquo to lsquo8EArsquo

Martelotta [33] 2 or 3 rotation averagewithin 120 area

optimal choice is 60 spacing for2 rotation average or 2x30 spac-ing for 3 rotation average

auditorium at10m distance

lsquo0-60rsquo lsquo0-30-60rsquo

000

020

040

060

080

100

120

140

160

180

200

single 0-40-80

29x125

2 EA 3 EA 4 EA 5 EA 6 EA 7 EA 8 EA 0-60

0-30-60

R

Standard

deviation[dB]

Rotational averaging method

500

10002000

4000

8000

Figure 4 Standard deviation of the sound level by stepwise rota-tions for a BampK 4292 measured at 7m distance in an anechoicroom in single octave bands from 500 to 8000Hz for variousaveraging methods (see Table IV for explanation of methods)R Repeated measurements without rotation

when measuring the sound level close to the sound sourcewhich is relevant for this paper However there is no agree-ment on which type of rotation average should be usedto find a sufficiently reliable average over the horizontalplane (while ignoring the fact that a single plane aver-age is not the same as a full sphere average) To inves-tigate the various rotational averaging methods impulseresponse measurements have been performed by the au-thors in an anechoic room at 7m distance using a dodeca-hedron loudspeaker BampK Type 4292 (see Annex for moredetails) For every rotation of 5 an impulse response wasdetermined resulting in 72 measurements Then for all av-eraging methods presented in Table IV every possible av-erage in sound level was determined (for instance in caseof a lsquo3 rotation average within a 120 area in steps of 40rsquo

the average could be determined 24 times) and its abso-lute deviation from the average over all 72 measurementsis calculated Linear interpolation was used when needingangles in between the 5 step Over all these possible abso-lute deviations within a certain rotational average methodthe standard deviation has been determined for each sepa-rate octave band from 500 to 8000Hz

Results are presented for the individual octave bands inFigure 4 for the BampK 4292 The standard deviation in-creases with frequency up and until 2 kHz while varia-tions in the 2 4 and 8 kHz bands are of the same order ofmagnitude To confirm that the results found for the BampK4292 are representative for dodecahedron loudspeakers ingeneral the ITA directivity data for various dodecahedronloudspeakers as presented in section III has been analysedand the average standard deviations for the 2 4 and 8 kHzoctave band are presented in Figure 5a for the moderatesize dodecahedron loudspeakers and in Figure 5b for thesmall size dodecahedron loudspeakers The standard devi-ation of 72 repeated measurements without rotation wasfound to be below 003 dB proving that the deviationsfound are indeed caused by directivity variations

43 Discussion on uncertainties due to directivityFrom our results of deviation in sound level for the varioussingle plane averaging methods as discussed in the previ-ous paragraph it can be concluded that an accurate esti-mation of the single plane average in single octave bandsabove 500Hz is not possible using a single random mea-surement The deviation from a full single plane averageis reduced significantly only for the ISO 3382-1 method(lsquo29x125rsquo) and the equal-angular rotations using 5 and

900


Standard

deviation[dB]

Standard

deviation[dB]

(a)

(b)


000

020

040

060

080

100

120

140

160

180

200

single 0-40-80

0-40-80

29x125

29x125

2 EA 3 EA 4 EA 5 EA 6 EA 7 EA 8 EA 0-60 0-30-60

0-30-60

R

R

000

020

040

060

080

100

120

140

160

180

200

single 2 EA 3 EA 4 EA 5 EA 6 EA 7 EA 8 EA 0-60

TUE

ITA1

ITA2

ITA3

ITA5

ITA4

ITA7

ITA8

Figure 5 Average standard deviation of the sound level by step-wise rotations for 2 4 and 8 kHz for various loudspeakers (a)moderate size dodecahedron loudspeakers (b) small size dodec-ahedron loudspeakers R Repeated measurements without rota-tion

7 steps (lsquo5EArsquo and lsquo7EArsquo) For the 5 steps equal-angularrotation the standard deviation introduced is 0 dB in theoctave bands up until 1 kHz and 01 02 and 03 dB at2 4 and 8 kHz respectively It should be noted that eventhough the result of a multiple step rotation average mayapproach the result of a single plane average results canstill deviate up to 2 dB from a full sphere average as men-tioned in Section 3 For laboratory calibration purposes itis therefore recommended to either measure a full sphereaverage if one is interested in accurate separate octaveband measurements or measure as many steps as possible(with 29 steps σ is below 01 dB) to determine the singleplane average if one is only interested in the single num-ber ratings mentioned in section IIIC However as we willdiscuss in the next section a single plane rotational aver-age with less averaging steps (only 5) can be a practicaltool when calibrating in the field

5 Field calibration measurements

The possibility of performing calibrations in the fieldhas been investigated The deviation of in-situ calibrationcompared to laboratory calibration has been reported byvarious researchers

51 Interference by the floor reflection

Gade stated in the appendix of his report on lsquoAcousticalSurvey of 11 European Concert hallsrsquo [23] that at first heused an in-situ calibration at 1 meter distance on stage tobe able to measureG while applying a time window to fil-ter out the direct sound together with the floor reflectionHe corrected the calibration level based on the theoreticaleffect of the floor reflection Afterwards when comparing

-30

-25

-20

-15

-10

-05

00

05

10

15

20

25

30

125 250 500 1000 2000 4000 8000

ΔLp[dB]

Frequency [Hz]

13 octave bands

11 octave bands

Figure 6 Effect of floor interference difference in SPL betweenthe average of two on stage measurements and a measurementin an anechoic room Results averaged over a full rotation in thehorizontal plane while producing a noise signal

the in-situ calibration to a reverberation room calibrationhe concluded that the theoretical correction did not predictthe actual deviation accurately As Gade noted the floorreflection does not increase the sound level equally in allfrequency bands Due to comb filtering some frequencieswill be amplified while others are cancelled out Figure 6shows the difference in SPL between the average of twoon stage measurements and a measurement in an anechoicroom in one-third-octave bands and full octave bands per-formed by the authors of this paper at 15m transducerheights The effect of interference can be clearly observedup to 500Hz Above 500Hz an average increase in SPLis found of 11 dB The interference effect is not visible inthe full octave band dataBeranek [34] also reports the difference between an in-

situ measurement using stationary noise measured withtwo microphone positions on either side of a dodecahe-dron sound source and a calibration performed in a re-verberation room see Table V Hak et al [5] showed re-sults for various cases among which are measurements at1 meter distance on stage of two concert hall stages seeFigure 7 A full rotation average was taken using station-ary noise and an 8 equal-angular step rotation average wastaken using impulse responses It should be noted that inthe latter actually a system calibration was performed andthe source to receiver distance was determined from theimpulse response causing a 15 cm deviation in distancedetermination More in-situ measurement were comparedto a calibration in an anechoic room by Dammerud [35]for G0minus10 using 29 averages of 124 steps in the anechoicroom and 4 single measurements at 1 meter distance on 8different stages A single measurement was taken per po-sition with the same rotation of the sound source relativeto the microphone for all measurements as suggested byGade [17] The various deviations found are summarisedin Table V together with an average offset and standarddeviation for the measurements that used a correct source-receiver distance All researchers used a 0ndash10ms timewindow on a stage with objects or surfaces beyond 4m dis-

901


Table V Overview of errors found by using an in-situ calibrations The physical distance was 10 m but the distance determinedfrom the impulse response and used in the system calibration was 085mΔLw ΔLw (error in Lw by in-situ calibration) 1 Theoretical[23] 2 Reverberation Room vs Stage [23] 3 Reverberation Room vs Stage [34] 4 Precision vs Stage Noise [5] 5 Precision vsStage System cal [5] 6 Anechoic vs 8 Stages [35] Avg Average over 2 3 4 and 6 (offsetinsitu) Std Standard deviation over 2 3 4and 6 (σinsitu)

Octave band with mid frequencies [Hz] AverageΔLw Int [ms] h [m] d [m] 125 250 500 1000 2000 4000 500ndash1000 250ndash2000

1 0ndash10 12 1 -4 17 -02 06 04 0 02 062 0-10 12 1 0 25 11 05 0 0 08 13 0-inf 15 1 27 22 17 11 09 04 14 154 0-inf 15 1 29 12 1 13 01 03 12 095 0-inf 15 1 -15 0 01 -01 06 08 0 026 0-10 10 1 -22 27 03 11 1 07 07 13Avg - 22 10 10 05 04 10 12Std 24 07 06 03 05 03 03 03

Figure 7 In-situ measurement setup on a concert hall stage witha source-receiver distance of 1m

-042

-021

000

022

045

125 250 500 1000 2000 4000 8000

ΔLw[dB]

Frequency [Hz]

a

b

c

d

e

Figure 8 Sound level per frequency measured on a concert hallstage at a distance of a 0950 b 0975 c 1000 d 1025 ande 1050 meter distance normalised to the 1000 distance mea-surement together with theoretical values derived using the in-verse square law 045 dB 022 dB 0 dB -021 dB and -042 dBrespectively

tance windowing out room reflections and reducing themaximum error by windowing to 01 dB (see Section 21)It is likely that the floor reflection is an important causefor these errors The variation in the measurements might

be explained by directivity problems of the sound sourceby different types of omnidirectional sound sources andby different transducer heights Other possible causes oferror might be microphone misplacements and other un-known variations due to moving the sound source and mi-crophone These possible causes of error will be discussedin the next two paragraphs

52 Microphone misplacement

The error due to transducers lsquomisplacementrsquo was investi-gated by Gehe in a master thesis [36] He found that theerror in G0minus10 due to his plusmn1 cm error in sound source tomicrophone distance would be negligible Earlier Gade[17] already concluded that a distance error of up to 30 cmwould lead to an error in the ST parameters of maximum1 dB Obviously such a large error in distance is nevermade when performing measurements accurately To in-vestigate the actual deviation in measured sound level dueto misplacement of the microphone the authors of thispaper measured the sound level using impulse responseswindowed for 0ndash10ms on a concert hall stage at a distanced of 0950 0975 1000 1025 and 1050 meter distance insteps of 25 cm (see Annex for more details) To reduce theerror due to directivity deviation a 5 equal-angular step-wise rotation average was used The transducers heightwas varied from 10 m 12m to 15m Figure 8 shows theresults for a 12m transducer height together with theoret-ical values based on the inverse square law 20 lg(d) It isclear that the measured results deviate from the theoreticalresults possibly due to the floor reflection but the resultsare close to the theoretical values for the 250 to 1000Hzoctave bands These results show that accurate placementof the transducers is necessary for direct field calibrationsWhen the microphone placement is done within 1 cm themaximum error can be expected to be below 01 dB andcan therefore be neglected

53 Variation over different positions and the influ-ence of objects

Gehe [36] also looked at the variation in measured ST ref-erence level at different positions on stage For 13 mea-

902


Table VI Overview of standard deviation of in-situ calibrations at different positions on stage A Gehe [36] with risers (13 positionsrotation aimed) B Dammerud [35] no risers (4 positions rotation aimed) C Dammerud [35] with risers (4 positions rotation aimed)D Concert hall empty stage (4 positions rotation random) E Concert hall empty stage (4 positions 5 step average) F Concert hallstage with chairs (4 positions 5 step average)


A 0-10 10 10 02B 0-10 10 10 02 02 01 01 03 02 01 01C 0-10 10 10 05 05 03 02 03 04 03 02D 0-10 135 10 01 01 01 04 24 16 03 06E 0-10 135 10 01 01 00 01 02 06 01 01F 0-10 135 10 05 03 02 08 10 08 05 05

surements spread over a stage the standard deviation inG0minus10 was only Δσ250minus2000 = 02 dB The variation ofG0minus10 over various positions was also determined for thedata from Dammerud [35] by the authors of this paperThe average standard deviation in G0minus10 over only 4 mea-surements is found to be σ250minus2000 = 01 dB for 2 stageswithout risers (in this context risers are devices to createheight differences on the stage) and σ250minus2000 = 02 dBfor 6 stages with risers In both cases such low standarddeviations are achieved as long as the exact same orienta-tion of the dodecahedron sound source towards the micro-phone is used and measurements on risers are performedwith both transducers on the same riser (and same height)We performed a similar study for various sets of our ownmeasurement data of stage acoustic measurements using adodecahedron loudspeaker During the measurements nospecial attention was given to aim the loudspeaker towardsthe microphone accurately because a 5 equal-angular steprotation average was used as a method to improve accu-racy see Section 4 On one stage the effect of chairs onthe measured deviation was investigatedIn Table VI all available results of per octave band

are presented A maximum σ = 06 dB per octave bandand σ = 02 dB for single number ratings is reached onstages without risers when aiming the sound source tothe microphone or taking a 5 equal angular step rotationaverage Risers introduce a slight increase in uncertaintywith a Δσ250minus2000 = 01 dB while chairs in (very) closeproximity to the transducers increase the uncertainty onlymoderately by Δσ250minus2000 = 04 dB As expected sin-gle measurements show a larger deviation at frequenciesabove 500Hz when the omnidirectional sound source isnot aimed at the microphone correctly a single measure-ment results in an σ250minus2000 of 06 dB while a 5 equal angu-lar step rotation average results in an average σ250minus2000 of01 dB Adding chairs in close proximity to the transducersresults in a σ250minus2000 of 05 dB

54 Discussion on field calibration methods

It can be concluded that the difference in laboratory andfield calibration methods found by different researchersvaries considerably The variance in the measurements bydifferent authors cannot be explained by the error due to

time windowing (maximum error 01 dB) and microphonemisplacement (maximum error 01 dB with 1 cm accu-racy) Performing multiple in-situ measurements in vari-ous halls using the same equipment results in a standarddeviation of 01ndash06 dB per octave band (on a flat stagefloor) which includes the time windowing uncertaintymicrophone misplacement uncertainty and the uncertaintydue to the source aiming for single measurements or thehorizontal plane averaging It is likely that the largest partof the deviations found between laboratory and field cal-ibration methods can be attributed to the floor reflectionThis means that a correction for the floor reflection isthe most important step to reduce the error The correc-tion should be determined by comparing the in-situ soundpower to a laboratory sound power using precision meth-odsTo determine the total uncertainty for the in-situ meth-

ods a model is defined that shows how the different iden-tified sources of uncertainty propagate through the mea-surement procedure While including a coverage factor of28 the in-situ method can be expressed by an offset andan average standard deviation by

U95insitu = offsetinsitu (3)

plusmn 28 σ2insitu + σ2

precision + σ2repositioning + σ2

rotation

and with laboratory correction

U95insitucorrected = (4)

plusmn 28 σ2precision + σ2

repositioning + σ2rotation

where U95insitu is the uncertainty of the in-situ method at95 confidence level in dB offsetinsitu and σinsitu is the av-erage systematic error and standard deviation due to in-situcalibration for 4 different researchers σprecision is the stan-dard deviation of the precision methods σrepositioning is thestandard deviation of 4 repeated measurements over differ-ent stages and σrotation is the standard deviation of the rota-tional averaging method (with a fixed aiming point σrotationis assumed to be 0)

The calculated uncertainty for the in-situ method with-out and with laboratory correction are shown in Table VIIin case of using a 5 equal-angular step rotation average

903


Table VII Uncertainty factors and calculated uncertainty for in-situ method without and with laboratory correction using precisionmethods Avg Single number ratings average (the 125-1000Hz and STI average were not calculated due to a lack of sufficient data) offset and deviation at 95 confidence level and 28 coverage factor deviation at 95 confidence level and 28 coveragefactor

Octave band with mid frequencies [Hz] Avg125 250 500 1000 2000 4000 500ndash1000 250ndash2000

offsetinsitu 0 22 10 10 05 04 10 12σinsitu 24 07 06 03 05 03 03 03σprecision 1 03 03 03 03 03 03 03σrepositioning 02 02 01 01 03 02 01 01σrotation 0 0 0 0 01 02 0 0U95insitu 0 22 1 1 05 04 12 1

plusmn73 plusmn22 plusmn19 plusmn12 plusmn19 plusmn14 plusmn12 plusmn12U95plane ll -73 0 -09 -02 -14 -1 0 -02U95plane ul 73 44 29 22 24 18 24 22U95insituminuscorrected plusmn29 plusmn1 plusmn09 plusmn09 plusmn12 plusmn12 plusmn09 plusmn09

It is clear that actual in-situ calibrations should be avoidedfor accurate level measurements because the uncertainty ofindividual octave band values and single numbers ratingsfor G and ST parameters is (much) larger than the param-etersrsquo JND However the in-situ method with laboratorycorrection as proposed by Gade where a fixed correctionvalue is used for the difference in laboratory and field cali-bration (see section IIB) seems promising in terms of be-ing both a reasonably accurate and practical method for thesingle number ratings Aiming the sound source to the mi-crophone or taking a 5 step rotation average without aim-ing both are an effective method to control the deviationin measured reference level between different positions onstage as long as the microphone is placed at the correctdistance within 1 cm The introduction of risers does notappear as a concern for measuring the reference level butchairs close to the transducers should be avoided To avoidthe introduction of any other uncertainties the signal pro-cessing should be kept identical after determining the fixedcorrection It should be noted that the in-situ method wasnot tested for calibration inside office spaces and thereforeno results are presented for STI

6 Conclusion

The results from above-mentioned existing and new re-search illustrate the concern about the accuracy of cal-ibrating the dodecahedron loudspeaker as an omnidirec-tional sound source for room acoustical measurements ofSound Strength (G) Speech Level (L) and Support (ST)type of parameters When measuring the sound power pro-duced by a dodecahedron loudspeaker as an omnidirec-tional sound source the effect of its directivity cannot beneglected and many other errors can be introduced espe-cially when calibrating in-situ We can discriminate be-tween three groups of calibration methods each with adifferent uncertainty for different frequency bands and forthe single number ratings for G LJ ST LpAS4m and STIFor each method and parameter the uncertainties are sum-marized in Table VIII

61 Precision methods

A laboratory calibration using precision methods like thereverberation room or intensity method results in an un-certainty of 28 dB at 125Hz and 08 dB in the frequencyrange 250ndash8000Hz The most practical method to achievea full sphere average is probably the reverberation roommethod as mentioned in ISO 3382-1 as was also recentlysuggested by Beranek and Nishihara [37] For single num-ber ratings the uncertainty varies between 08 and 14 dBThe precision methods can be sufficiently accurate to beable to calibrate the sound source for measuring the roomacoustic parameters G ST and LpAS4m because theirJNDrsquos are larger than the uncertainty except for the sep-arate 125Hz octave band Single number ratings for pa-rameters that are sensitive for the large uncertainty at the125Hz octave like the STI and LJ have an uncertaintygt 1 dB For measuring STI the uncertainty of the preci-sion method is slightly larger than the JND This holds forthe worst case scenario where the room acoustics has noinfluence (anechoic room) In practice the uncertainty dueto calibration for measuring STI will be (just) below theJND

62 Single plane free field method

The method mentioned in ISO 3382-1 where the soundpower is determined from 125 degree steps while rotat-ing in the horizontal plane is conceptually clear but it re-sults in a systematic error Above 1000Hz we showeddeviations up to 2 dB per octave band between the sin-gle plane free field method and a full sphere measurementbased on measurements of 9 different dodecahedron loud-speakers It is clear that the deviation can be significantlyimproved by reducing the dodecahedronrsquos diameter but asound power measurement should always cover the fullsphere if one is interested in separate octave bands Formeasuring single number ratings for G ST and STI theuncertainty of a single plane average is on average 33more than the precision methods

904


Table VIII Summary of measurement uncertainty at 95 confidence level of different calibration methods for moderate size dodeca-hedron loudspeakers Precision method ISO 3740 reverberation room or intensity probe over sphere or free field over sphere Singleplane free field method as suggested by ISO 3382-3 using a full rotation average or 29 steps of 125 degrees In-situ measurement ona stage floor without risers or chairs 0-10 ms time window microphone placement accuracy 1 cm a fixed source to microphone aimingpoint or 5 equal-angular rotation average In-situ corrected As in-situ measurement with additional correction for difference betweenlaboratory precision measurement and in-situ measurement The maximum uncertainty over all octave bands is shown which isdominated by the 125Hz octave band For uncertainties per octave band see Table III and Table VII The uncertainty presented forSTI holds for the worst case scenario when the room acoustics has no influence The uncertainty due to calibration for measuring STImight be lower than presented The two figures represent the offset and the random deviation

Type of calibration UncertaintyFrequency octave bands LJ ST G LpAS4m STI

JND 1ndash2 dB - 2 dB 1 dB 1 dB

Precision method ISO 3740 le plusmn28 plusmn14 plusmn08 plusmn08 plusmn11Single plane free field method le plusmn28 0 -02 01 -03

plusmn14 plusmn09 plusmn09 plusmn12In-situ measurement le plusmn73 - 12 1 -

plusmn12 plusmn12In-situ corrected plusmn29 - plusmn09 plusmn09 -

63 In-situ measurement

We have shown that an in-situ calibration at 1m distanceis not accurate with un uncertainty of plusmn73 dB for separatebands and +24 dB for single number ratings G and ST The systematic deviation between the in-situ measurementand a laboratory calibration can be corrected if the erroris known for the particular sound source and transducersrsquoheight This can be useful in circumstances where the ac-tual sound power of the source is difficult to reproduce foreach different measurement condition The correction be-tween the laboratory calibration and in-situ calibration canbe determined using a full rotation average (using a 125

steps average resulting in 29 measurements or using an av-erage over 5 equal-angular rotation steps) or by determin-ing the correction between the laboratory calibration andthe in-situ measurement at 1m for a fixed sound sourceaiming point and fixed height (as suggested by Gade [17])Results from various researchers have shown that the sin-gle number ratings of measured results using both the rota-tional average or fixed aiming point method can be repro-duced with 03 dB standard deviation over different mea-surement points on a single stage with and without ris-ers and over stages in different halls However the in-situ method including laboratory correction should onlybe used for measuring single number ratings for G and STand it should not be used in case one is interested in sepa-rate octave bands

64 Conclusion

Based on the JND for single number ratings an uncer-tainty lt10 dB would be desired for measuring G and STIand an uncertaintylt 20 dB for measuring STearly of ST lateIt is clear that even the most accurate calibration processesdescribed in this paper have uncertainties that are in thesame order of magnitude of the parametersrsquo JND Thismight seem as if these calibration processes are sufficiently

accurate However it should not be overseen that perform-ing an accurate sound power calibration is just the first stepin taking an accurate measurement of the room acousticparameters For instance the directivity of the dodecahe-dron sound source will still influence the measurement re-sult with errors well above 10 dB [4 30 31 32] Withcurrent available measurement methods it still might notbe possible for room acoustical parameters that use thesound power as a reference level to be measured accu-rately enough

Appendix

Measurement equipment

For our measurements the same measurement set wasused The power amplifier had a built-in white noise gen-erator For every measurement this noise generator was setto exactly the same value so the sound power level of theomnidirectional sound source was always the same Thesound source was a 12 loudspeaker omnidirectional soundsource (dodecahedron) with a diameter of approx 40 cmThe measurement equipment consisted of the followingcomponentsbull sound source omnidirectional (BampK Type 4292) di-

rectivity in compliance with ISO 3382bull signals stationary white noise and an exponentially

swept sinebull inputoutput USB audio device (Acoustics Engineer-

ing - Triton)bull power amplifier (Acoustics Engineering - Amphion)bull turntable 80 s for one rotation (BampK Type 2305)bull microphone 12 omnidirectional ICP (BampK Type

4189)bull sound intensity probe (BampK Type 3520)bull software DIRAC (BampK Type 7841)

905


Diffuse-field measurement conditions

The diffuse-field measurements were carried out in the re-verberation room (200m3) of the Faculty of Applied Sci-ences of the Delft University of Technology All soundpower measurements were done according to ISO 3741According to this standard two source positions and fourmicrophone positions were used for the direct methodFor the system calibration measurements (impulse re-sponse measurement using e-sweeps and deconvolution)two sound source positions and three microphone posi-tions were used For each situation the measurement re-sults were averaged over the microphone and sound sourcepositions

Sound Intensity measurements

The sound intensity measurements were carried out in theanechoic room of the Faculty of Applied Sciences of theDelft University of Technology The measurements wereperformed according to ISO 9614-3 using a metal meshcube with dimensions 105 times 105 times 105m3 and a meshsize of 15 times 15 cm2 Using the sweep scan method all in-dividual surfaces were scanned in two directions and av-eraged to one intensity measurement The sound intensityof the bottom surface was determined by turning the om-nidirectional sound source upside down The total soundpower level is obtained by summing the 6 separate soundintensity results

Free-field measurement conditions

The free-field measurements were also carried out in theanechoic room of the Faculty of Applied Sciences of theDelft University of Technology In this room a measure-ment is performed at 1m distance (near field) and 7m dis-tance from the centre of the omnidirectional sound sourceFor both distances full rotational measurements were per-formed using stationary white noise while rotating thesound source around its vertical axis using a turntable witha rotation speed of 36080 s For the stepwise rotationalmeasurements exponential sweep signals were used to de-termine an impulse response

In situ measurement conditions

The measurements in situ were carried out on the stageof the symphonic concert hall and the chamber music hallof the Frits Philips Muziekcentrum Eindhoven The (near-field) measurements are performed at a distance of 1mfrom the centre of the omnidirectional sound source Dur-ing the measurements the stages were unoccupied

Signal processing

The impulse response is calculated through deconvolutionof the roomrsquos response to a stimulus signal with the stim-ulus signal itself The result is a time domain signal whichis filtered using band-pass filters as recommended by ISO3382-1 and using the reverse filtering technique The fil-ters are IEC 61260-compliant full and third octave fre-quency band filters To enable accurate measurements of

very short reverberation times time reversed filtering isused Following ISO 3382-1 the impulse response startingpoint is determined from the broadband impulse responsesand defined as the point where the signal level first risesabove 20 dB below the maximum level However in allfree field measurements presented in this paper the sourceto receiver distance was measured by the distance betweenthe physical centre of the dodecahedron sound source andthe microphone (without using information from the im-pulse response)

Acknowledgement

We would like to thank Ingo Witew for generously shar-ing his directivity data from the loudspeakers measured atITA and Jens Dammerud for sharing his data measuredon stages The authors wish to thank Han Vertegaal andJan Hak from Acoustics Engineering for their support indeveloping the measurement systems This project wasfunded by the Netherlands Organisation for Scientific Re-search (NWO)

References

[1] ISO 3382 Acoustics ndash Measurement of room acoustic pa-rameters International Organisation for Standardisation(ISO) Geneva (CH) 2009

[2] IEC 60268-162003 Sound system equipment ndash Part 16Objective rating of speech intelligibility by speech trans-mission index International Electrotechnical CommissionGeneva (CH) 2003

[3] ISO 3382-3-2012 Acoustics ndash Measurement of roomacoustic parameters ndash Part 3 Open plan spaces Inter-national Organisation for Standardisation (ISO) Geneva(CH) 2012

[4] A Lundeby T E Vigran H Bietz M Vorlaumlnder Uncer-tainties of measurements in room acoustics Acustica 81(1995) 344ndash355

[5] C C J M Hak R H C Wenmaekers J P M Hak L C Jvan Luxemburg A C Gade Sound strength calibrationmethods Proceedings of ICA Sydney 2010

[6] P Lehmann Uumlber die Ermittlung raumakustischer Krite-rien und deren Zusammenhang mit subjektiven Beurteilun-gen der Houmlrsamkeit PhD Thesis Technical UniversityBerlin 1976

[7] M Barron L J Lee Energy relations in concert auditori-ums I J Acoust Soc Am 84 (1988) 618ndash628

[8] C C J M Hak R H C Wenmaekers L C J van Lux-emburg Measuring room impulse responses impact of thedecay range on derived room acoustic parameters ActaAcustica united with Acustica 98 (2012) 907ndash915

[9] P Virjonen J Keraumlnen V Hongisto Determination ofacoustical conditions in open-plan offices proposal for newmeasurement method and target values Acta Acusticaunited with Acustica 95 (2009) 279ndash290

[10] J S Bradley R Reich S G Norcross A just noticeabledifference in C50 for speech Applied Acoustics 58 (1999)99ndash108

[11] R H C Wenmaekers N H A M van Hout L C J vanLuxemburg C C J M Hak The effect of room acousticson the measured speech privacy in two typical Europeanopen plan offices Proceedings of Internoise Ottawa 2009

906


[12] A C Gade Investigations of musiciansrsquo room acousticconditions in concert halls I Methods and laboratory ex-periments Acustica 69 (1989) 193ndash203

[13] A C Gade Investigations of musiciansrsquo room acousticconditions in concert halls II Field experiments and syn-thesis of results Acustica 69 (1989) 249ndash261

[14] R H C Wenmaekers C C J M Hak L C J van Luxem-burg On measurements of stage acoustic parameters - timeinterval limits and various source-receiver distances ActaAcustica united with Acustica 98 (2012) 776ndash789

[15] K Ueno K Kato K Kawai Effect of room acoustics onmusiciansrsquo performance Part I Experimental investigationwith a conceptual model Acta Acustica united with Acus-tica 96 (2010) 505ndash515

[16] R H C Wenmaekers C C J M Hak H P J C de VosBinaural sound exposure by the direct sound of the ownmusical instrument Proceedings of ISRA 2013 Toronto2013

[17] A C Gade Practical aspects of room acoustic measure-ments on orchestra platforms Proceedings of 14th ICABeijing 1992

[18] A C Gade Estimated value obtained from a personal con-versation with AC Gade in 2009

[19] ISO 37402000 Acoustics ndash Determination of sound powerlevels of noise sources ndash Guidelines for the use of basicstandards International Organisation for Standardisation(ISO) Geneva (CH) 2000

[20] M Aretz R Orlowski Sound strength and reverberationtime in small concert halls Appl Acoustics 70 (2009)1099ndash1110

[21] J J Dammerud Stage acoustics for orchestras in concerthalls PhD Thesis University of Bath 2009

[22] ISO 37411999 Acoustics ndash Determination of sound powerlevels of noise sources using sound pressure ndash Precisionmethods for reverberation rooms International Organisa-tion for Standardisation (ISO) Geneva (CH) 1999

[23] A C Gade Acoustical survey of eleven European con-cert halls Report No44 Technical University of Denmark1989

[24] L Beranek Subjective rank-orderings and acoustical mea-surements for fifty-eight concert halls Acta Acusticaunited with Acustica 89 (2003) 494ndash508

[25] J J Dammerud M Barron Attenuation of direct soundand the contributions of early reflections within symphonyorchestras J Acoust Soc Am 128 (2010) 1755ndash1765

[26] R San Martiacuten M Arana J Machiacuten A Arregui Impulsesource versus dodecahedral loudspeaker for measuring pa-rameters derived from the impulse response in room acous-tics J Acoust Soc Am 134 (2013) 275ndash284

[27] M Vorlaumlnder G Raabe Calibration of reference soundsources Acustica 81 (1995) 247ndash263

[28] I 9614-32002

[29] I B Witew G K Behler Uncertainties in measurement ofsingle number parameters in room acoustics Proc ForumAcusticum Budapest Hungary 2005

[30] T W Leishman S Rollins H M Smith An experimentalevaluation of regular polyhedron loudspeakers as omnidi-rectional sources of sound J Acoust Soc Am 120 (2006)1411ndash1422

[31] R San Martiacuten I B Witew M Arana M Vorlaumlnder In-fluence of the source orientation on the measurement ofacoustic parameters Acta Acustica united with Acustica93 (2007) 387ndash397

[32] C C J M Hak R H C Wenmaekers J P M Hak L C Jvan Luxemburg The source directivity of a dodecahedronsound source determined by stepwise rotation Proceedingsof Forum Acusticum Aalborg 2011

[33] F Martellotta Optimizing stepwise rotation of dodecahe-dron sound source to improve the accuracy of room acous-tic measures J Acoust Soc Am 134 (2013) 2037ndash2048

[34] L Beranek Concert halls and opera houses Music acous-tics and architecture Springer Verlag New York 2004

[35] J J Dammerud The ST measures without the standardreference level White paper available online june 2013wwwstageacwordpresscomarticles

[36] C A Gehe Maringling av ST paring scenen i konsertsaler Mas-ter Thesis Norges Teknisk-naturvitenskapelige UniversitetNTNU Norway 2013

[37] L Beranek N Nishihara Mean-free-paths in concert andchamber music halls and the correct method for calibrat-ing dodecahedral sound sources J Acoust Soc Am 135(2014) 223ndash230

907


ever in earlier research we have shown that different meth-ods to obtain the free field SPL may yield different resultswith deviations more than 2 dB for individual octave bands[5] The low standard deviations found by Lundeby et al[4] between 8 different measurement teams are thereforehighly questionableThe deviations in sound power determination are prob-

lematic as one would like to measure most room acous-tic parameters within the limits of their Just NoticeableDifference (JND) which can be as low as 1 dB for somelevel parameters It is necessary to find out when measure-ment methods are sufficiently accurate and which methodsshould be avoided In this paper the difference betweenvarious calibration methods and the impact of simplifica-tions within these methods are investigated This is doneby using available data from literature and to close someknowledge gaps or to check whether the findings from lit-erature can be reproduced by performing additional mea-surements or analysing shared data from other researchersIn some cases results are only available from one sin-gle research(er) using one single loudspeaker type whichis often dodecahedrally shaped We did not perform suchextensive amount of measurements necessary to signifi-cantly identify all uncertainty contributions in each mea-surement method but the main conclusions are based onresults from multiple investigations involving various re-searchers and sound sources The overview presented inthis paper provides valuable insight in the merits of soundsource calibration for room acoustic purposes and somemajor problems have been identifiedIn this paper the background on the most relevant room

acoustic parameters and common calibration methods isdiscussed in Section 2 In Section 3 the differences ofvarious laboratory measurement methods concerning thesound power as a reference for room acoustic parametersare discussed Findings from literature and new researchhave been combined to investigate uncertainties In Sec-tion 4 problems with the directivity of the sound sourceare discussed which is particularly important for the cali-bration methods that only measure in the horizontal planeof the sound source while taking rotational averages InSection 5 in-situ measurement methods are discussed in-cluding (floor) interference effects and variations over dif-ferent positions In Section 6 the paper will conclude witha summary and conclusions on the uncertainty that can beexpected from using the available methods

2 Background

21 Room acoustic parameters and sound power

The sound strength G is used to investigate the sound dis-tribution in a concert hall or to compare the sound levelsbetween different concert halls Originally Lehmann in-troduced the Staumlrkemass or lsquoStrenght Indexrsquo which wasdefined as the difference in SPL in the hall caused by anomnidirectional sound source on the stage and the soundpower level Lw of the same sound source [6] Later on Gwas defined as the SPL at a listener position in the hall

with reference to the SPL at 10m distance from the samesound source in a free field The late lateral sound energylevel LJ is similar to G in its definition of the referencelevel Here the late sound energy arriving after 80ms at afigure-of-eight microphone is compared to the total soundenergy at 10m distance at an omnidirectional microphonein the free field For G the 10 meter distance was chosenby Barron and Lee for reasons of convenience because thischoice will often result in measured values of the soundlevel Lp close to the reference value Lp10m and hence val-ues of G close to 0 dB [7] G can either be determined us-ing stationary noise or using impulse responses [1] wherethe sound pressure exposure levelLpE is determined (up tothe time point that the energy decay or Impulse to NoiseRatio (INR) [8] is 30 dB or lower) The single numberrating for G is calculated from the average of the 500 and1000Hz octave band defined by ISO 3382-1 as GM andthe Just Noticeable Difference (JND) is 1 dB For LJ thesingle number rating is calculated from the average of the125 to 1000Hz octave band denoted by LJavg The JNDfor LJ is unknown

LpAS4m is the A-weighted SPL of normal speech at4 meter distance from an omnidirectional sound sourceLpAS4m is used together with D2S the decay of soundper doubling of the distance to describe the decay ofspeech sound in an open plan office A standardised spec-tral level LpS1m(f ) defined at 1 meter distance is usedto describe the sound power of the normal speaker [3]After A-weighting the speech spectrum the sound levelin dB(A) is predominantly dependent on the level in the500 and 1000Hz octave bands The distance of 4m is cho-sen as a nominal distance where the far field starts [9]In a similar way the absolute SPL of speech is used inthe calculation of the Speech Transmission Index (STI)where the SPL of the received speech LpS(f ) and the SPLdue to background noise LeqN (f ) is used to determinethe signal to noise ratio (SNR) In both LpAS4m and STIparameters the sound power of the sound source mustbe known to be able to apply the standardised spectrumand level The JND for the STI is 003 [10] The impactof reverberation on STI is small in open plan offices asshown by Wenmaekers et al [11] In a worst case sce-nario where reverberation does not affect the STI calcula-tion and the influence of background noise is fully domi-nant we can translate the JND of the STI as a JND of theSNR in dB In this way the maximum possible error inSignal level (or speech level LpS ) due to calibration un-certainty can be investigated In this paper the individualerrorsΔLpS(f ) in dB over the octave bands 125 to 8000Hzare translated into a modulation transfer index MTI(f ) by(ΔLpS(f )+15)30 The MTI(f ) is weighted in accordancewith IEC 60268-16 and the STI is calculated Then to ar-rive at a weighted single-number rating errorΔLpSsingle iscalculated as (STItimes30)minus15 dB A difference of 003 in STIappears at approximately 1 dB difference in ΔLpS single

The stage acoustic parameters Early Support STearlyand Late Support ST late are used to investigate the ensem-ble conditions and perceived reverberance by musicians on

893



















894


























895







(a)

(b)

(c)




896





ΔLw[dB]

-20

-15

-10

-05

00

05

10

15

20

125 250 500 1000 2000 4000 8000

ΔLw[dB]


(a)

(b)

(c)

ΔLw[dB]

ΔLw[dB]

Frequency [Hz]

(d)

-20

-15

-10

-05

00

05

10

15

20

125 250 500 1000 2000 4000 8000

Diffuse

Intensity

-20

-15

-10

-05

00

05

10

15

20

125 250 500 1000 2000 4000 8000


-20

-15

-10

-05

00

05

10

15

20

125 250 500 1000 2000 4000 8000

ITA4

ITA7

ITA8


897
















and


precision (2)



898













899






-




-


area in steps of 5



lsquosinglersquo



lsquo0-40-80rsquo



lsquo29x125rsquo









000

020

040

060

080

100

120

140

160

180

200

single 0-40-80

29x125

2 EA 3 EA 4 EA 5 EA 6 EA 7 EA 8 EA 0-60

0-30-60

R

Standard

deviation[dB]


500

10002000

4000

8000






900


Standard

deviation[dB]

Standard

deviation[dB]

(a)

(b)


000

020

040

060

080

100

120

140

160

180

200

single 0-40-80

0-40-80

29x125

29x125

2 EA 3 EA 4 EA 5 EA 6 EA 7 EA 8 EA 0-60 0-30-60

0-30-60

R

R

000

020

040

060

080

100

120

140

160

180

200


TUE

ITA1

ITA2

ITA3

ITA5

ITA4

ITA7

ITA8







-30

-25

-20

-15

-10

-05

00

05

10

15

20

25

30

125 250 500 1000 2000 4000 8000

ΔLp[dB]

Frequency [Hz]

13 octave bands

11 octave bands




901






-042

-021

000

022

045

125 250 500 1000 2000 4000 8000

ΔLw[dB]

Frequency [Hz]

a

b

c

d

e








902




A 0-10 10 10 02B 0-10 10 10 02 02 01 01 03 02 01 01C 0-10 10 10 05 05 03 02 03 04 03 02D 0-10 135 10 01 01 01 04 24 16 03 06E 0-10 135 10 01 01 00 01 02 06 01 01F 0-10 135 10 05 03 02 08 10 08 05 05










rotation







903







6 Conclusion






904











64 Conclusion



Appendix







905










Signal processing



Acknowledgement


References












906


















[28] I 9614-32002










907



















894


























895







(a)

(b)

(c)




896





ΔLw[dB]

-20

-15

-10

-05

00

05

10

15

20

125 250 500 1000 2000 4000 8000

ΔLw[dB]


(a)

(b)

(c)

ΔLw[dB]

ΔLw[dB]

Frequency [Hz]

(d)

-20

-15

-10

-05

00

05

10

15

20

125 250 500 1000 2000 4000 8000

Diffuse

Intensity

-20

-15

-10

-05

00

05

10

15

20

125 250 500 1000 2000 4000 8000


-20

-15

-10

-05

00

05

10

15

20

125 250 500 1000 2000 4000 8000

ITA4

ITA7

ITA8


897
















and


precision (2)



898













899






-




-


area in steps of 5



lsquosinglersquo



lsquo0-40-80rsquo



lsquo29x125rsquo









000

020

040

060

080

100

120

140

160

180

200

single 0-40-80

29x125

2 EA 3 EA 4 EA 5 EA 6 EA 7 EA 8 EA 0-60

0-30-60

R

Standard

deviation[dB]


500

10002000

4000

8000






900


Standard

deviation[dB]

Standard

deviation[dB]

(a)

(b)


000

020

040

060

080

100

120

140

160

180

200

single 0-40-80

0-40-80

29x125

29x125

2 EA 3 EA 4 EA 5 EA 6 EA 7 EA 8 EA 0-60 0-30-60

0-30-60

R

R

000

020

040

060

080

100

120

140

160

180

200


TUE

ITA1

ITA2

ITA3

ITA5

ITA4

ITA7

ITA8







-30

-25

-20

-15

-10

-05

00

05

10

15

20

25

30

125 250 500 1000 2000 4000 8000

ΔLp[dB]

Frequency [Hz]

13 octave bands

11 octave bands




901






-042

-021

000

022

045

125 250 500 1000 2000 4000 8000

ΔLw[dB]

Frequency [Hz]

a

b

c

d

e








902




A 0-10 10 10 02B 0-10 10 10 02 02 01 01 03 02 01 01C 0-10 10 10 05 05 03 02 03 04 03 02D 0-10 135 10 01 01 01 04 24 16 03 06E 0-10 135 10 01 01 00 01 02 06 01 01F 0-10 135 10 05 03 02 08 10 08 05 05










rotation







903







6 Conclusion






904











64 Conclusion



Appendix







905










Signal processing



Acknowledgement


References












906


















[28] I 9614-32002










907


























895







(a)

(b)

(c)




896





ΔLw[dB]

-20

-15

-10

-05

00

05

10

15

20

125 250 500 1000 2000 4000 8000

ΔLw[dB]


(a)

(b)

(c)

ΔLw[dB]

ΔLw[dB]

Frequency [Hz]

(d)

-20

-15

-10

-05

00

05

10

15

20

125 250 500 1000 2000 4000 8000

Diffuse

Intensity

-20

-15

-10

-05

00

05

10

15

20

125 250 500 1000 2000 4000 8000


-20

-15

-10

-05

00

05

10

15

20

125 250 500 1000 2000 4000 8000

ITA4

ITA7

ITA8


897
















and


precision (2)



898













899






-




-


area in steps of 5



lsquosinglersquo



lsquo0-40-80rsquo



lsquo29x125rsquo









000

020

040

060

080

100

120

140

160

180

200

single 0-40-80

29x125

2 EA 3 EA 4 EA 5 EA 6 EA 7 EA 8 EA 0-60

0-30-60

R

Standard

deviation[dB]


500

10002000

4000

8000






900


Standard

deviation[dB]

Standard

deviation[dB]

(a)

(b)


000

020

040

060

080

100

120

140

160

180

200

single 0-40-80

0-40-80

29x125

29x125

2 EA 3 EA 4 EA 5 EA 6 EA 7 EA 8 EA 0-60 0-30-60

0-30-60

R

R

000

020

040

060

080

100

120

140

160

180

200


TUE

ITA1

ITA2

ITA3

ITA5

ITA4

ITA7

ITA8







-30

-25

-20

-15

-10

-05

00

05

10

15

20

25

30

125 250 500 1000 2000 4000 8000

ΔLp[dB]

Frequency [Hz]

13 octave bands

11 octave bands




901






-042

-021

000

022

045

125 250 500 1000 2000 4000 8000

ΔLw[dB]

Frequency [Hz]

a

b

c

d

e








902




A 0-10 10 10 02B 0-10 10 10 02 02 01 01 03 02 01 01C 0-10 10 10 05 05 03 02 03 04 03 02D 0-10 135 10 01 01 01 04 24 16 03 06E 0-10 135 10 01 01 00 01 02 06 01 01F 0-10 135 10 05 03 02 08 10 08 05 05










rotation







903







6 Conclusion






904











64 Conclusion



Appendix







905










Signal processing



Acknowledgement


References












906


















[28] I 9614-32002










907







(a)

(b)

(c)




896





ΔLw[dB]

-20

-15

-10

-05

00

05

10

15

20

125 250 500 1000 2000 4000 8000

ΔLw[dB]


(a)

(b)

(c)

ΔLw[dB]

ΔLw[dB]

Frequency [Hz]

(d)

-20

-15

-10

-05

00

05

10

15

20

125 250 500 1000 2000 4000 8000

Diffuse

Intensity

-20

-15

-10

-05

00

05

10

15

20

125 250 500 1000 2000 4000 8000


-20

-15

-10

-05

00

05

10

15

20

125 250 500 1000 2000 4000 8000

ITA4

ITA7

ITA8


897
















and


precision (2)



898













899






-




-


area in steps of 5



lsquosinglersquo



lsquo0-40-80rsquo



lsquo29x125rsquo









000

020

040

060

080

100

120

140

160

180

200

single 0-40-80

29x125

2 EA 3 EA 4 EA 5 EA 6 EA 7 EA 8 EA 0-60

0-30-60

R

Standard

deviation[dB]


500

10002000

4000

8000






900


Standard

deviation[dB]

Standard

deviation[dB]

(a)

(b)


000

020

040

060

080

100

120

140

160

180

200

single 0-40-80

0-40-80

29x125

29x125

2 EA 3 EA 4 EA 5 EA 6 EA 7 EA 8 EA 0-60 0-30-60

0-30-60

R

R

000

020

040

060

080

100

120

140

160

180

200


TUE

ITA1

ITA2

ITA3

ITA5

ITA4

ITA7

ITA8







-30

-25

-20

-15

-10

-05

00

05

10

15

20

25

30

125 250 500 1000 2000 4000 8000

ΔLp[dB]

Frequency [Hz]

13 octave bands

11 octave bands




901






-042

-021

000

022

045

125 250 500 1000 2000 4000 8000

ΔLw[dB]

Frequency [Hz]

a

b

c

d

e








902




A 0-10 10 10 02B 0-10 10 10 02 02 01 01 03 02 01 01C 0-10 10 10 05 05 03 02 03 04 03 02D 0-10 135 10 01 01 01 04 24 16 03 06E 0-10 135 10 01 01 00 01 02 06 01 01F 0-10 135 10 05 03 02 08 10 08 05 05










rotation







903







6 Conclusion






904











64 Conclusion



Appendix







905










Signal processing



Acknowledgement


References












906


















[28] I 9614-32002










907





ΔLw[dB]

-20

-15

-10

-05

00

05

10

15

20

125 250 500 1000 2000 4000 8000

ΔLw[dB]


(a)

(b)

(c)

ΔLw[dB]

ΔLw[dB]

Frequency [Hz]

(d)

-20

-15

-10

-05

00

05

10

15

20

125 250 500 1000 2000 4000 8000

Diffuse

Intensity

-20

-15

-10

-05

00

05

10

15

20

125 250 500 1000 2000 4000 8000


-20

-15

-10

-05

00

05

10

15

20

125 250 500 1000 2000 4000 8000

ITA4

ITA7

ITA8


897
















and


precision (2)



898













899






-




-


area in steps of 5



lsquosinglersquo



lsquo0-40-80rsquo



lsquo29x125rsquo









000

020

040

060

080

100

120

140

160

180

200

single 0-40-80

29x125

2 EA 3 EA 4 EA 5 EA 6 EA 7 EA 8 EA 0-60

0-30-60

R

Standard

deviation[dB]


500

10002000

4000

8000






900


Standard

deviation[dB]

Standard

deviation[dB]

(a)

(b)


000

020

040

060

080

100

120

140

160

180

200

single 0-40-80

0-40-80

29x125

29x125

2 EA 3 EA 4 EA 5 EA 6 EA 7 EA 8 EA 0-60 0-30-60

0-30-60

R

R

000

020

040

060

080

100

120

140

160

180

200


TUE

ITA1

ITA2

ITA3

ITA5

ITA4

ITA7

ITA8







-30

-25

-20

-15

-10

-05

00

05

10

15

20

25

30

125 250 500 1000 2000 4000 8000

ΔLp[dB]

Frequency [Hz]

13 octave bands

11 octave bands




901






-042

-021

000

022

045

125 250 500 1000 2000 4000 8000

ΔLw[dB]

Frequency [Hz]

a

b

c

d

e








902




A 0-10 10 10 02B 0-10 10 10 02 02 01 01 03 02 01 01C 0-10 10 10 05 05 03 02 03 04 03 02D 0-10 135 10 01 01 01 04 24 16 03 06E 0-10 135 10 01 01 00 01 02 06 01 01F 0-10 135 10 05 03 02 08 10 08 05 05










rotation







903







6 Conclusion






904











64 Conclusion



Appendix







905










Signal processing



Acknowledgement


References












906


















[28] I 9614-32002










907
















and


precision (2)



898













899






-




-


area in steps of 5



lsquosinglersquo



lsquo0-40-80rsquo



lsquo29x125rsquo









000

020

040

060

080

100

120

140

160

180

200

single 0-40-80

29x125

2 EA 3 EA 4 EA 5 EA 6 EA 7 EA 8 EA 0-60

0-30-60

R

Standard

deviation[dB]


500

10002000

4000

8000






900


Standard

deviation[dB]

Standard

deviation[dB]

(a)

(b)


000

020

040

060

080

100

120

140

160

180

200

single 0-40-80

0-40-80

29x125

29x125

2 EA 3 EA 4 EA 5 EA 6 EA 7 EA 8 EA 0-60 0-30-60

0-30-60

R

R

000

020

040

060

080

100

120

140

160

180

200


TUE

ITA1

ITA2

ITA3

ITA5

ITA4

ITA7

ITA8







-30

-25

-20

-15

-10

-05

00

05

10

15

20

25

30

125 250 500 1000 2000 4000 8000

ΔLp[dB]

Frequency [Hz]

13 octave bands

11 octave bands




901






-042

-021

000

022

045

125 250 500 1000 2000 4000 8000

ΔLw[dB]

Frequency [Hz]

a

b

c

d

e








902




A 0-10 10 10 02B 0-10 10 10 02 02 01 01 03 02 01 01C 0-10 10 10 05 05 03 02 03 04 03 02D 0-10 135 10 01 01 01 04 24 16 03 06E 0-10 135 10 01 01 00 01 02 06 01 01F 0-10 135 10 05 03 02 08 10 08 05 05










rotation







903







6 Conclusion






904











64 Conclusion



Appendix







905










Signal processing



Acknowledgement


References












906


















[28] I 9614-32002










907













899






-




-


area in steps of 5



lsquosinglersquo



lsquo0-40-80rsquo



lsquo29x125rsquo









000

020

040

060

080

100

120

140

160

180

200

single 0-40-80

29x125

2 EA 3 EA 4 EA 5 EA 6 EA 7 EA 8 EA 0-60

0-30-60

R

Standard

deviation[dB]


500

10002000

4000

8000






900


Standard

deviation[dB]

Standard

deviation[dB]

(a)

(b)


000

020

040

060

080

100

120

140

160

180

200

single 0-40-80

0-40-80

29x125

29x125

2 EA 3 EA 4 EA 5 EA 6 EA 7 EA 8 EA 0-60 0-30-60

0-30-60

R

R

000

020

040

060

080

100

120

140

160

180

200


TUE

ITA1

ITA2

ITA3

ITA5

ITA4

ITA7

ITA8







-30

-25

-20

-15

-10

-05

00

05

10

15

20

25

30

125 250 500 1000 2000 4000 8000

ΔLp[dB]

Frequency [Hz]

13 octave bands

11 octave bands




901






-042

-021

000

022

045

125 250 500 1000 2000 4000 8000

ΔLw[dB]

Frequency [Hz]

a

b

c

d

e








902




A 0-10 10 10 02B 0-10 10 10 02 02 01 01 03 02 01 01C 0-10 10 10 05 05 03 02 03 04 03 02D 0-10 135 10 01 01 01 04 24 16 03 06E 0-10 135 10 01 01 00 01 02 06 01 01F 0-10 135 10 05 03 02 08 10 08 05 05










rotation







903







6 Conclusion






904











64 Conclusion



Appendix







905










Signal processing



Acknowledgement


References












906


















[28] I 9614-32002










907






-




-


area in steps of 5



lsquosinglersquo



lsquo0-40-80rsquo



lsquo29x125rsquo









000

020

040

060

080

100

120

140

160

180

200

single 0-40-80

29x125

2 EA 3 EA 4 EA 5 EA 6 EA 7 EA 8 EA 0-60

0-30-60

R

Standard

deviation[dB]


500

10002000

4000

8000






900


Standard

deviation[dB]

Standard

deviation[dB]

(a)

(b)


000

020

040

060

080

100

120

140

160

180

200

single 0-40-80

0-40-80

29x125

29x125

2 EA 3 EA 4 EA 5 EA 6 EA 7 EA 8 EA 0-60 0-30-60

0-30-60

R

R

000

020

040

060

080

100

120

140

160

180

200


TUE

ITA1

ITA2

ITA3

ITA5

ITA4

ITA7

ITA8







-30

-25

-20

-15

-10

-05

00

05

10

15

20

25

30

125 250 500 1000 2000 4000 8000

ΔLp[dB]

Frequency [Hz]

13 octave bands

11 octave bands




901






-042

-021

000

022

045

125 250 500 1000 2000 4000 8000

ΔLw[dB]

Frequency [Hz]

a

b

c

d

e








902




A 0-10 10 10 02B 0-10 10 10 02 02 01 01 03 02 01 01C 0-10 10 10 05 05 03 02 03 04 03 02D 0-10 135 10 01 01 01 04 24 16 03 06E 0-10 135 10 01 01 00 01 02 06 01 01F 0-10 135 10 05 03 02 08 10 08 05 05










rotation







903







6 Conclusion






904











64 Conclusion



Appendix







905










Signal processing



Acknowledgement


References












906


















[28] I 9614-32002










907


Standard

deviation[dB]

Standard

deviation[dB]

(a)

(b)


000

020

040

060

080

100

120

140

160

180

200

single 0-40-80

0-40-80

29x125

29x125

2 EA 3 EA 4 EA 5 EA 6 EA 7 EA 8 EA 0-60 0-30-60

0-30-60

R

R

000

020

040

060

080

100

120

140

160

180

200


TUE

ITA1

ITA2

ITA3

ITA5

ITA4

ITA7

ITA8







-30

-25

-20

-15

-10

-05

00

05

10

15

20

25

30

125 250 500 1000 2000 4000 8000

ΔLp[dB]

Frequency [Hz]

13 octave bands

11 octave bands




901






-042

-021

000

022

045

125 250 500 1000 2000 4000 8000

ΔLw[dB]

Frequency [Hz]

a

b

c

d

e








902




A 0-10 10 10 02B 0-10 10 10 02 02 01 01 03 02 01 01C 0-10 10 10 05 05 03 02 03 04 03 02D 0-10 135 10 01 01 01 04 24 16 03 06E 0-10 135 10 01 01 00 01 02 06 01 01F 0-10 135 10 05 03 02 08 10 08 05 05










rotation







903







6 Conclusion






904











64 Conclusion



Appendix







905










Signal processing



Acknowledgement


References












906


















[28] I 9614-32002










907






-042

-021

000

022

045

125 250 500 1000 2000 4000 8000

ΔLw[dB]

Frequency [Hz]

a

b

c

d

e








902




A 0-10 10 10 02B 0-10 10 10 02 02 01 01 03 02 01 01C 0-10 10 10 05 05 03 02 03 04 03 02D 0-10 135 10 01 01 01 04 24 16 03 06E 0-10 135 10 01 01 00 01 02 06 01 01F 0-10 135 10 05 03 02 08 10 08 05 05










rotation







903







6 Conclusion






904











64 Conclusion



Appendix







905










Signal processing



Acknowledgement


References












906


















[28] I 9614-32002










907




A 0-10 10 10 02B 0-10 10 10 02 02 01 01 03 02 01 01C 0-10 10 10 05 05 03 02 03 04 03 02D 0-10 135 10 01 01 01 04 24 16 03 06E 0-10 135 10 01 01 00 01 02 06 01 01F 0-10 135 10 05 03 02 08 10 08 05 05










rotation







903







6 Conclusion






904











64 Conclusion



Appendix







905










Signal processing



Acknowledgement


References












906


















[28] I 9614-32002










907







6 Conclusion






904











64 Conclusion



Appendix







905










Signal processing



Acknowledgement


References












906


















[28] I 9614-32002










907











64 Conclusion



Appendix







905










Signal processing



Acknowledgement


References












906


















[28] I 9614-32002










907










Signal processing



Acknowledgement


References












906


















[28] I 9614-32002










907


















[28] I 9614-32002










907

The Sound Power as aReference forSound Strength (G...

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