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SOUND PROPAGATIONOUTDOORS

SESSIONS

Developments in Modelling and Measuring GroundImpedanceK. AttenboroughDept. of Engineering, The University of Hull, Hull HU6 7RX: e-mail; [email protected] for representing the acoustical properties of the ground surface are reviewed in the light of recent data. Thedistinct influences of surface roughness are described. A full description requires information about the mean heightand spacing of surface roughness as well as porosity, tortuosity, connected pore geometry, flow resistivity and layering.There is a trade-off between simplicity and accuracy. Progress towards in situ methods for ground characterization isoutlined. The various alternative approaches involve measurement of short range propagation, level difference spectratemplates or direct deduction of complex surface impedance.

MODELS FOR GROUNDIMPEDANCEAtmospheric sound propagation close to theground is sensitive to the acoustical properties ofthe ground surface as well as to meteorologicalconditions. Surface porosity allows sound topenetrate and hence to be both absorbed andundergo phase change through friction andthermal exchanges. There is interference betweensound traveling directly between source andreceiver and sound reflected from the ground. Thisinterference is known as ground effect [1,2]. Overporous surfaces, enhancement tends to occur atlow frequencies since the longer wavelengths areless able it is to penetrate the pores. The presenceof vegetation tends to make the surface layer ofground including the root zone more porous.Outdoor surfaces are likely to be rough as well aporous. Roughness effects have been modellednumerically by the Boundary Element Method andanalytically by boss theory [3]. The influence ofroughness that is small compared with the incidentwavelengths may be represented through effectiveimpedance [3,4].Various models and parameters have been usedto calculate the impedance of smooth groundsurfaces. The most important characteristic of aground surface that affects its acoustical characteris its flow resistivity or air permeability.A widely used model for the acousticalproperties of outdoor surfaces involves a singleparameter, the effective flow resistivity, tocharacterise the ground.

This single-parameter model [5], describes thepropagation constant, k and normalised surfaceimpedance, Z in terms of a single adjustableparameter known as the effective flow resistivity,e. The propagation constant and normalisedsurfaceimpedancearegivenbyk 0.700 0.595(1a)]= [1 + 0.0978( f e )+ i 0.189( f e )k1

Z=

1c1 0.754 0.732(1b)= 1 + 0.0571( f e )+ i 0.087( f e )c

Harmonic time dependence, eit, is understood.There is considerable evidence that (1a) tends tooverestimate the attenuation within a porousmaterial with high flow resistivity. Moresophisticated theoretical models for the acousticalproperties of rigid-porous materials introduceporosity, the tortuosity (or twistiness) of thepores, factors related to pore shapes and sizes, andmultiple layering [6-10].A model based on an exponential change inporosity with depth [7,9] has enabled betteragreement with measured data for the acousticalproperties of many outdoor ground surfaces than(1). The two adjustable parameters are theeffective flow resistivity (Re), which differs frome, and the effective rate of change of porositywith depth (e). The impedance of the groundsurface is predicted byRe ic 0 e ,1+ i(2)Z=

f

f

+

8f

where e = (n' +2)/ and n' is a grain shapefactor such that the tortuosity is given by n .

SESSIONS

2

2

where V is the roughness volume per unit area ofsurface (equivalent to mean roughness height), bis the mean center-to-center spacing, is aninteraction factor depending on the roughnessshape and packing density and k is the wavenumber.The same approach can be extended to give theeffective normalised surface admittance of a poroussurface containing 2-D roughness [4,11]. In general,the effective admittance is predicted to be a functionof the observer geometry. A tolerably successfulprediction of the effective normalised impedance ofa rough porous surface is that of the smooth surfacebut with a reduced real part.

MEASUREMENT OF GROUNDIMPEDANCEMeasurements of the magnitude of the excessattenuation from a point source at non-grazingincidence may be inverted, by means of leastsquares or template fitting to impedance modelsand yield impedance as a function of frequency.As well as not requiring the assumption of planewaves, which is valid only at sufficient sourceheight and near normal incidence, the short-rangepropagation method also includes effects of smallscale surface roughness.Fig. 1 shows measurements obtained overuncultivated grassland, using a direct impedancefitting method [12,13] Note that the impedance,deduced from measured complex excessattenuation spectra, tends to zero above 3 kHz.

Roughness i.e. incoherent scatter, may explain thesemeasurements.

REAL

20

10

0- IMAGINARY

A boss model approach has been used to dealwith coherent (in phase) and incoherent scatterfrom a rough surface [3]. As long as the soundwavelength is significantly larger than meanheight and spacing of the roughness, it predictsthat the roughness of the surface of anacoustically-hard material produces a non-zeroeffective admittance. For grazing incidence on ahard surface containing randomly distributed 2-Droughness normal to the roughness axes, theeffective admittance may be written 3V 2 k 3 b 2 (3)1 + iVk ( 1) =

10

20100

31 .10FREQUENCY Hz

41 .10

FIGURE 1. Normalised impedance data (open circles)obtained over established grassland. Solid lines representpredictions including roughness. Dotted lines arepredictions without roughness.REFERENCES1. TFW Embleton, JE Piercy, N Olson, J. Acoust. Soc.Am. 59, 267-77 (1976).2. K. Attenborough, Appl. Acoust. 24, 289-319 (1988).3. P. Boulanger, K. Attenborough, S. Taherzadeh, T. F.Waters-Fuller, K. M. Li, J. Acoust. Soc. Am. 104, 147482 (1998).4. K. Attenborough, S. Taherzadeh, J. Acoust. Soc. Am.98:1717-22 (1995).5. M.E. Delany and E. N. Bazley, Appl. Acoust. 3, 105-16(1970).6. K. Attenborough, J. Sound Vib. 99, 521-44 (1985).7. K. Attenborough J. Acoust. Soc. Am. 92, 418-27(1992).8. K. Attenborough, Acta Acust. 1, 213-26 (1993).9. R. Raspet, J. M. Sabatier, J. Acoust. Soc. Am., 99, 14752 (1996).10. K. V. Horoshenkov, K. Attenborough and S. N.Chandler-Wilde J. Acoust. Soc. Am., 104, 1198-209(1998).11. K. Attenborough, T. F. Waters-Fuller, J. Acoust. Soc.Am. 108, 949-56 (2000).12. S. Taherzadeh and K. Attenborough, J. Acoust. Soc.Am. 105, 2039-42 (1999).13. K. Attenborough, T. F. Waters-Fuller, K. M. Li and J.A. Lines, J. Agric. Engng. Res. 76, 183-95 (2000).

SESSIONS

Sound propagation above an impedance discontinuityin the presence of meteorological effects,using a BEM formulationE. Premat, J. DefranceDepartment of Environmental Acoustics, Centre Scientifique et Technique du Btiment,24 rue Joseph Fourier, 38400 St Martin dHres, France, [email protected]

Using the same approach as in Meteo-BEM [1, 2], a new model is derived for describing outdoor sound propagation above animpedance discontinuity in refracting conditions. It is based on a Boundary Integral Equation formulation including ground andmeteorological effects in the Greens function. The methodology is presented. Results are given, showing that this approach canbe used for complex outdoor sound propagation prediction.

1. INTRODUCTION

MS

Complex traffic noise problems involve soundpropagation from low height sources above impedancediscontinuities in the presence of meteorologicaleffects. A number of studies have been presented inthe past in order to develop models for predicting theeffect of mixed impedance on sound propagation overa flat ground [3]. Most of these works have dealt witha quiescent atmosphere, except for a few models basedon the Parabolic Equation approach [4] that can takerefraction effects into account. The aim of this paper isto use the Boundary Integral Equation theory (BIE) toinvestigate the problem of outdoor sound propagationin a stratified atmosphere above an impedancediscontinuity. Following the same approach as inMeteo-BEM [1, 2] ground and meteorological effectsare included in the Greens function of the BIE.Section 2 recalls briefly the BIE theory used fordescribing sound propagation above an impedancediscontinuity. Then section 3 presents the Greensfunction accounting for meteorological effects. Section4 gives results and finally we conclude and giveperspectives.

2. THE BOUNDARY INTEGRALEQUATION FOR SOUNDPROPAGATION OVER ANIMPEDANCE DISCONTINUITYThe BIE theory represents a very powerful tool inorder to assess for any kind of shape and absorption ofthe propagation domain boundaries (in particularuneven terrains, various shapes of sound barriers,impedance discontinuities).

P2

1

FIGURE 1. Geometrical configuration for theproblem of impedance discontinuityWe consider here the case of an infinitely longcoherent line source parallel to the impedancediscontinuity (figure 1). This cylindrical wavepropagation problem is mathematically equivalent to atwo-dimensional problem. In order to solve theboundary value problem (consisting of the Helmholtzequation and suitable boundary conditions), thefollowing boundary integral equation can bederived [5]:p (S, M ) = G 2 (S, M ) + ik ( 2 1 ) G 2 (M , P )p(S,P )d (P )

(1)where p is the acoustic pressure, k represents the wavenumber, S the source and M the receiver. G1,respectively G2, denotes the Greens function for theacoustic field above a flat boundary of homogeneousadmittance 1, respectively 2. is the part of theground of 1 admittance.The integration is over the interval . When the pointM approaches , an integral equation is obtained,whose solution (p(S,P) for P on ) allows one tocalculate the acoustic pressure at any receiver position.This Boundary Integral Equation can be solvedaccurately using the Boundary Element Method(BEM) [5]. Following an idea of Chandler-Wilde [6], a

SESSIONS

2

with :

K = k G 1 (S, P )G 2 (M , P ) d (P ) (3)

The integral K can be directly evaluated using forinstance the composite midpoint rule or one can followthe improved calculation method proposed in [6]. Thisapproach has already been derived for a quiescentatmosphere but if one uses the appropriate Greensfunction presented in section 3, the case of soundpropagation above an impedance discontinuity canthen be studied in refracting conditions with thisformulation.

3. THE GREENS FUNCTIONACCOUNTING FORMETEOROLOGICAL EFFECTSWe consider here the case of downward refraction. Inthe case of a positive constant sound speed profile, weuse for the Greens function of the BIE the NormalModes solution (linear source), with the samenotations as in [7]:

p S (r, z ) =

exp(ik n r ) Ai( n + z s / l )Ai( n + z / l )i222l nk n n [Ai( n )] Ai ' ( n )

(

)

[

]

n = k k lare the zeros of Ai' (n ) + qAi( n ) = 0where

2n

20

2

(4)

S(0,zs) denotes the source, M(r,z) is the receiver. knrepresents the horizontal wave number of the nth mode.The Normal Modes solution is particularly attractivefor the BIE since the variables involved in theanalytical formulation are uncoupled and thederivatives of the Greens function are straightforwardto derive.

4. RESULTS AND CONCLUSIONFigure 2 shows the influence of downward refraction(linear sound speed profile : c(z) = c0(1+az), with a =2.9 10-3 m-1 compared to the case a = 0 m-1 for aquiescent atmosphere) in the presence of an impedancediscontinuity 20 m away from the source (zS = z = 1m, f = 500 Hz, (1,2) = (300000 cgs, 300 cgs)). Theresults show that the Boundary Integral Equationtheory can be adapted to complex atmospheric sound

propagation problems. More realistic sound speedprofiles are going to be studied and scale modelmeasurements will be undertaken for validation of thisnew model.15

Excess Attenuation (dB)

good approximation, which gives correct results and isless computationally expensive, consists of assumingthat the acoustic pressure in can be approximated bywhat it would be if the whole boundary had admittance1. This yields the following approximation top(S,M) :(2)p(S, M ) = G (S, M ) + i( 2 1 )K

105051012(1,2)12(1,2)

15202530

a = 0 m-1

a = 2.9 10-3 m-1

10

10

220

30

40

50

60

70

80

90

100

Source - receiver distance (m)FIGURE 2. Influence of downward refractionabove a mixed impedance ground.f=500Hz, zS=z=1m, 1=300000cgs, 2=300cgs,distance source-impedance discontinuity : 20m, a=0(homogeneous atmosphere) or 2.9 10-3 m-1(downwardrefraction).

REFERENCES1. E. Premat, Y. Gabillet, A new boundary element methodfor predicting outdoor sound propagation andapplication to the case of a sound barrier in the presenceof downward refraction, Journal of the AcousticalSociety of America, 108 (6), 2000, pp. 2775-2783.2. E. Premat, Y. Gabillet, J. Defrance, Applications of theMeteo-BEM model in downward and upward refractingconditions, 9th International Symposium on LongRange Sound Propagation, TNO, The Hague, 2000, 13p.3. P. Boulanger, et al, Models and measurements of soundpropagation from a point source over mixed impedanceground, Journal of the Acoustical Society of America,102 (3), 1997, pp. 1432-1442.4. J.S. Robertson, P.J. Schlatter, W.L. Siegmann, Soundpropagation over impedance discontinuities with theparabolic approximation, Journal of the AcousticalSociety of America, 97, 1996, pp. 761-767.5. D. Habault,Soundpropagationaboveaninhomogeneous plane : boundary integral equationmethods, Journal of Sound and Vibration, 100, 1985,pp. 55-67.6. J.N.B. Harriott, S.N.B. Chanler-Wilde, D.C. Hothersall,Long-distance sound propagation over an impedancediscontinuity, Journal of Sound and Vibration, 148 (3),1991, pp. 365-380.7. R. Raspet, G. Baird, W. Wu, Normal mode solution forlow frequency sound propagation in a downwardrefracting atmosphere above a complex impedanceplane, Journal of the Acoustical Society of America, 91,1992, pp. 1341-1352.

SESSIONS

Meteorological Aspects of Sound Propagation Modelingover Irregular TerrainD. Heimann , R. BlumrichDLR Institute of Atmospheric Physics, Oberpfaffenhofen, 82234 Weling, F.R.GermanyExamples of coupled 3D meteorological and acoustical simulations are presented. Numerical experiments illustrate how topographical and meteorological effects act together. It is shown that topographical effects on the atmosphere cannot be neglected. Inparticular, the validity of the effective sound speed concept is tested, which is frequently used in PE-type propagation models.z

INTRODUCTION

EXAMPLE 1: NOISE SCREENThe 3D simulation deals with a 3 m high noisescreen which ends inside a 40 m 20 m wide modeldomain. A coherent line source of 250 Hz is placed5 cm above hard ground, 6.5 m in front of the screen(see Figure 1).The large-scale wind is assumed to flow parallelto the x-axis with 5 m/s at 10 m above ground. Theatmospheric model simulates how the air flowsaround the obstacle. The Euler-type linearized numerical model [1] of acoustical wave propagationconsiders the screen and the airflow which is distorted by the screen in all its spatial componentsFigure 2 shows how the sound field is influencedby the screen. The 250 Hz tone gives rise to variousinterference patterns. In order to analyse the efficiency of the screen under different wind situations,

line source

y

screen

line source

xFIGURE 1. Schematic vertical cross section (top) andplane view (bottom) of the screen and the flow across it.distance from screen edge - y in m

The propagation of sound waves is subject toground effects and atmospheric influences. The atmosphere in turn is influenced by the ground throughthe exchange of energy, momentum and mass (ofwater). As a consequence, all parameters that act onthe sound as it propagates over irregular terrain aremore or less range-dependent. Acoustical simulationsover long ranges have to account for these influencesin an appropriate way.In the following two examples are presented: theeffect of a noise screen in the presence of wind andthe sound propagation around a hill under differentmeteorological conditions. In either case the acoustical simulation is preceded by the simulation of theatmospheric response to the respective topographicalfeature.Different model experiments are performed todemonstrate the atmospheric effects.

distance from screen - x in m

FIGURE 2. Plane view of sound pressure level (6dBintervals; 1.5 m above ground). Downwind case.

distance from screen - x in m

FIGURE 3: Efficiency of the screen in the case of no wind(solid), downwind (dashed), and upwind (dot-dashed).

SESSIONS

the sound pressure was averaged in y-direction between -10 m < y < 0 and 0 < y < 10 m. The efficiencyof the screen near its edge is shown in Figure 3.Although the sound level is generally highest (lowest) under the condition of downwind (upwind), theefficiency of the screen is highest under upwind condition between the screen and x = 15 m.

EXAMPLE 2: HILLIn the following example a meteorological mesoscale model is used to provide three-dimensionalhigh-resolution fields of wind, temperature and humidity near a 50 m high hill for given large-scalemeteorological situations. A point source (1002000 Hz) is located 25 m above the hill top (Figure 4). The ground has a finite impedance. The meteorological fields are taken as input in a ray-basedsound propagation model. The coupled models allowa consistent simulation of ground and air effects.

z

FIGURE 6. Horizontal of the deviation of Exp. A nometeo (solid lines), B effective sound speed - homogeneous (broken lines) and C effective sound speed - inhomogeneous (dashed-dotted lines) from Exp. D full meteo .

point sourceA Lagrange-type sound particle model [2] wasused to simulate the propagation of sound outsideshadow zones in 3D (Figure 5). Different modelexperiments were performed in which the meteorological fields were fully considered or partly approximated. The results along the axes shown inFigure 5 reveal the differences (Figure 6).

y

CONCLUSIONSx

'crosswind' profile

FIGURE 4. Schematic vertical cross section (top) andplane view (bottom) of the hill and the flow across it.

'upwind' profile

'downwind' profile

The meteorological mesoscale simulations showthat the wind field is distinctively affected by thetopography leading to a strong acceleration above ascreen or a hill. Moreover, the flow is divertedaround the hill in the case of low Froude number,while the air flows over the hill with correspondingupward and downward motion in the case of highFroude number.The acoustical simulations suggest that the stateof the atmosphere has a significant effect on thesound level and may not be neglected. The effectivesound speed approach turned out to be an acceptableapproximation provided the atmospheric inhomogeneities are considered.

REFERENCES1.

2.

FIGURE 5. Horizontal distribution of sound level (dB) fora strong-wind situation.

Blumrich R., D. Heimann, A Eulerian sound propagationmodel for studies of complex meteorological effects. Submitted to J.Acoust.Soc.Am. (2001)Heimann D.and G. Gross, Coupled simulation of meteorological parameters and sound level in a narrow valley. Applied Acoustics, 56, 73-100 (1999).

SESSIONS

A Study of Range-Dependent Meteorological Conditionsand their Influences on Outdoor Sound PropagationD.C.Waddington and Y.W.LamAcoustics Research Centre, School of Acoustics and Electronic Engineering,University of Salford, Salford M5 4WT, UKA series of field trials to enable simultaneous detailed range-dependent meteorological and acoustical measurementsare under way. A high-power omni-directional electro-acoustic source is used to provide a broadband sound power of130dB and the sites allow measurements over well-defined terrains of around 1km. To ensure that sufficient details ofthe sound propagation are resolved, ten independent computer-based measurement systems are installed atapproximately 100m intervals to make time-synchronised measurements. Correlations between the comprehensivepropagation and meteorological data obtained so far are presented in this paper.

INTRODUCTIONSalford has recently acquired a meteorologicalDoppler infrared LIDAR system that is capable ofmaking fast scans of aerosol backscatter and aerosolradial wind velocity from which atmosphericturbulence parameters may be derived. This offers, forthe first time, the possibility of simultaneous detailedmeasurement of meteorological and noise propagationdata. The objective of present research is to establishthe variability of meteorological conditions and theirsignificance on outdoor noise propagation along avariety of propagation paths with a distance up to 1km.The project involves the development and verificationof an outdoor noise prediction model that can take intoaccount range-dependent meteorological conditions.Realization of these project objectives involves aseries of field trials in which noise propagationmeasurements are made simultaneously withmeteorological data under a range of weatherconditions over well-defined terrain. Discussed hereare the results of the first of these field trials.

FLAT TERRAIN FIELD TRIALThe acoustical measurement systems were numbered#1 to #10 from the source. Each station was used as astand-alone data logger and audio recorder logging Leq,Lfast and 1/3-octave band spectra each second.Synchronised digital recordings made for 10 minuteseach hour sampled a maximum audio frequency of10kHz. Measurements were made over a period of a

week, with the source operating for eight hours a day.Automatic weather stations were set-up on 10m maststo provide spot checks of meteorological conditions.The measured noise data were synchronized withmeasurements from the meteorological Dopplerinfrared LIDAR system to enable direct correlation.The LIDAR is installed at a suitable position to scanthe atmosphere for meteorological data during thenoise measurement period. Local meteorologicalstations were used to provide wind profilesmeasurements to check against the LIDAR data.

DESCRIPTION OF MEASUREMENTSThe sound source used a series of equalised pink noise,silences and tones. Although meteorological data wasrecorded by the automatic weather stations and radiosonde, regrettably no measurements were obtainedfrom the LIDAR during this trial. The windsthroughout the trial period were strong cross winds tothe line of the acoustic array. The consequences werehigh wind noise on the microphones and littlerefraction in the line of the receivers.

COMPARISON WITH PREDICTIONThe parabolic equation method [1] provides accurateanalytical predictions particularly useful forcomparisons with the measurements of propagationfrom the tones used in the investigation. Howevermore practical for environmental noise applications isthe JASPEN [2] model using a heuristic ray tracingmethod [3]. Although assuming a linear velocitygradient to determine the sound propagation paths, for

SESSIONS

60

variation in the Leq (30s) measured in the 500Hz 1/3octave band with vector wind speed determined at thesource position is shown in figure 2 for three of the tenreceiver positions. A spread of measured sound levelof around 6dB at 229m is seen not to significantlydiffer at receivers further from the source, and theleast-squares fit to the data for each receiver distancesdoes not show a correlation between the vector windspeed and measured sound level. While these databroadly support the relationships drawn from analysisof the measurement observations of the JOULE trials[5], where the dependence of the measured sound levelon the vector wind speed was too weak and the spreadtoo large to be conclusive, due in part to the restrictedrange of vector wind speeds encountered during thistrial these results do not resolve the problemsidentified by this earlier work.

50

CONCLUSIONS

distances less that 1km the model has been shown tohave accuracy comparable with that of the PE method[4]. Figure 1 compares JASPEN predictions of LAeqwith background compensated measurements of pinknoise at each receiver. Though the vector wind speedwas close to zero, the wind velocity was typicallyaround 10m/s100

90

Leq dB(A)

80

70

40

0

100

200

300

400500600700Receiver distance (m)

800

900

1000 1100

FIGURE 1. Comparison with JASPEN prediction (O)5452

1k Hz 1/3 oc tave Leq (30s ) dB

5048

Useful investigations into the characterisation ofmeteorological conditions for outdoor soundpropagation prediction purposes have in the past beenlimited by the ability to accurately determine the windspeed profile. The first of a series of trials designed tostudy range-dependent meteorological conditions andtheir influences on outdoor sound propagation hasbeen performed. Whilst the analysis of this field trialdata was limited by the absence of range-dependentmeteorology, further trials over various terrains areunder way to address these sound propagation topics.

4644

ACKNOWLEDGEMENTS

4240383634-5

-4.5

-4

-3.5

-3-2.5-2-1.5Vec tor wind s peed (m /s )

-1

-0.5

0

FIGURE 2. Showing the variation in measured 500Hz1/3 octave band with vector wind speed for receiverdistances 229m (+), 454m (O) and 789m (*).

CORRELATION WITHMETEOROLOGYA correlation analysis between sound pressure leveland vector wind speed and various wind andtemperature gradients has shown that the highestcorrelation is with the vector wind speed [5]. The

The Acoustics Research Team of DERA Malvernkindly provided the trial site for the above work. Theauthors wish to thank Kevin Brown of PowerGen PlcUK for predictions using the JASPEN program. Thiswork was performed under a UK EPSRC grant numberGR/M71459.

REFERENCES1. Gilbert, K., West, M. and Sack, R.A., Appl.Acoustics 37,31-49 (1992)2. Brown, K., Evolution of geometric ray tracing model andcomparison with loudspeaker measurements, MSc thesis,University of Salford 20003. L'Esprance, A., Herzog, P., Daigle G.A. and Nicolas,J.R. Appl. Acoustics 37, 111-139 (1992).4. Lam,Y.W. Int. J. Acoustics and Vib. 5, 135-139 (2000).5. LamY.W. Eighth International Congress On Sound AndVibration, Hong Kong (2001)

SESSIONS

Source Location by Ground Effect InversionQiang Wanga, Keith Attenborougha and Richard Brindba

Department of Engineering, University of Hull, Hull HU6 7RX, UKDERA Winfrith Technology Centre, Dorchester, Dorset DT2 8XJ, UK

b

A ground effect inversion and localization algorithm (GEILA) for source localization in an unknown outdoor environment hasbeen investigated. GEILA matches the complex acoustic pressure received simultaneously at a distributed microphone array.Tests on simulated data have shown the possibility of deducing both range and height of broad-band sources in refracting andturbulent conditions. The method is robust to changing environments. Alternatively, for known source positions, the algorithmcan be used to deduce acoustical properties of the ground surface and meteorological parameters.

INTRODUCTION

120r=229m110

FLUCTUATION OF SPLThe instantaneous sound pressure level (SPL)fluctuates under different environmental conditions inthe presence of atmospheric refraction and turbulenceabove an impedance ground. Figure 1 shows examplesof SPL spectra obtained during 2 seconds ofmeasurement at a range of 229 m, with source andreceiver at 2m and 1.5 m [5]. The fluctuation of SPLresults from variation in sound velocity gradient [2]due to turbulence. Li et al fitted the ground effect dipin instantaneous level difference spectra for groundimpedance parameters and fitted the first two dips forsound velocity gradients [2]. Their results demonstratethat the fluctuations in the best-fit sound velocitygradients and ground impedance parameters are relatedto the fluctuations of SPL.

100

Sound pressure level(dB)

Considerable progress has been made in adaptingnumerical techniques for predictions of soundpropagation in the presence of refraction andatmospheric turbulence above an impedance ground[1-3]. However, localization of an acoustical source inan outdoor environment including the refraction andturbulence is still in progress. Li et al developed analgorithm for determination of source height using avertical array of two microphones by ground effectinversion from a priori knowledge of a range betweensource and receivers in the presence of a linear soundvelocity gradient [4]. The purpose of this work is toinvestigate localization of sources in an unknownoutdoor environment using a ground effect inversionand localization algorithm (GEILA) based onpropagation models that include ground effect andatmospheric refraction. The effects of turbulence havebeen taken into account implicitly.

90

80

70

60

50

40

30

2

3

10

10Frequency (Hz)

FIGURE 1. Sound pressure level obtained during a 2-secondmeasurement. zs = 2m , z = 1.5m and r = 229m . The linesare instantaneous SPL spectra (one spectrum every 0.16 s).

DESCRIPTION OF GEILAGEILA makes use of a multi-element microphonearray, equivalent to three single arrays each containingseveral microphones separated vertically and arrangedin an arbitrarily-shaped triangle, see Figure 2. Amatched field processing method, i.e. Bartlettprocessor, which was developed for the underwaterenvironment [6], matches complex acoustic pressurespectra received simultaneously on each microphone ofthese arrays with those predicted by a propagationmodel for a grid of possible source positions (r, z s ) .The estimation includes the instantaneous effects ofsound velocity gradient and ground impedance on thesource localization. The values of sound velocitygradient a and ground impedance parameters e and e can be deduced by environmental inversion.However, the deduced values a , e and e representeffective values corresponding to instantaneous soundpressure spectra rather than true values average overtime in a natural atmosphere.

SESSIONS

Table 1. Numerical results deduced by GEILA in simulateddownward refraction.

r

(m)

FIGURE 2. Geometry (x-y view) of a multi-element arrayand source.

NUMERICAL RESULTSIt is assumed that the atmosphere is verticallystratified and linear sound velocity profiles are used todescribe the atmospheric refraction. In the presence ofturbulence, sound velocity profiles fluctuate about theirmean profile. Corresponding to each instantaneoussound velocity profile, there are instantaneous soundpressure spectra. GEILA matches each instantaneouscomplex sound pressure, which is simulated by using aGF-PE propagation model, with those predicted by apropagation model (either ray-trace or residue series)for a source location for trial values of r , zs , a , eand e .Table 1 shows numerical results for r , zs , a , eand e deduced from GEILA using frequencies 5001500 Hz. The complex SPL, due to a broad bandsource at r = 1 000 m and z s = 20 m above a ground-1

surface ( e = 105 mks rayls m -1 and e = 15 m ), issimulated in sound velocity gradient a that fluctuatesrandomly from 0.16 106 m -1 to 8.32 106 m -1 due tolow turbulence. Three microphones of each verticalarray are separated at heights of 0.1, 2 and 3 m abovethe ground. Using three such vertical arrays (see Figure2), we should be able to determine the source azimuth [7]. Table 2 shows the results for the same geometrybut in conditions where the simulated sound velocitygradient a fluctuates randomly from 0.12 106 m -1to 91.3 106 m -1 .

SUMMARYThe numerical results of this study have shown thepossibility of deducing range and height of a fixedsource in refracting and turbulent conditions.

95096096010009509509809509801000950

z s

(m)1918182019191919201818

a

a

(m )

(m )

10

10

1

6

0.160.330.981.001.211.531.852.783.695.268.32

1

6

e

e

(rayls m ) (m )-1

-1

10 4

0.110.250.801.01.01.01.52.03.14.58.0

10109101010101010119

1515151515151515152015

Table 2. Numerical results deduced by GEILA in simulatedupward refraction.r

(m)980950960100096095095010409609701010

z s

(m)1919192019181715152217

a

(m )1

a

e

(m ) (rayls m )1

10 6

10

-0.12-0.31-0.65-1.00-1.45-3.28-8.11-13.9-40.3-52.8-91.3

-0.10-0.10-0.10-1.00-1.00-3.0-7.0-10.0-30.0-64.0-100

-1

6

10

4

1010101010101011131010

e

(m )-1

1515151515151520201515

ACKNOWLEDGEMENTThis work was supported by DERA ContractSSDW2/4395.

REFERENCES1.T. Hidaka, K. Kageyama, and S. Masuda, J. Acoust. Soc.Jn, 6 117-125 (1985).2.A. LEsperance, Y. Gabillet, and G. A. Daigle, J. Acoust.Soc. Am. 98, 570-579 (1995).3.E. M. Salomons, V. E. Ostashev, S. F. Clifford, and R. L.Lataitis, J. Acoust. Soc. Am. 109, 1881-1893 (2001).4.K. M. Li, K. Attenborough, and N. W. Heap, J. Sound Vib.145, 111-128 (1991).5.D. C. Waddington, Salford University, 2000.6.R. M. Hamson and M. A. Ainslie, J. Computation Acoust.6, 45-59 (1998).7.Q. Wang, K. Attenborough and R. Brind, ICSV8proceedings (2001).

SESSIONS

Calculation of Sound Propagation over Non Flat Terrain usingParabolic Equation

N. Blairon , Ph. Blanc-Benon , M. Brengier and D. JuvCentre Acoustique, LMFA UMR CNRS 5509, Ecole Centrale de Lyon BP 163, 69131 Ecully Cedex, FranceL.C.P.C. - Centre de Nantes, Route de Bouaye, BP 4129, 44341 Bouguenais Cedex, France

In this paper we develop a method which aims to evaluate the propagation of an acoustic wave above a non flat ground andwhich could include realistic outdoor conditions. The acoustic waves are propagated in a parabolic approximation. The effect oftopography is taken into account by rotating the coordinate system. Our method is validated in the case of propagation above aconvex cylinder. Then an application of our method to the acoustic propagation above a wedge is presented.

INTRODUCTIONDue to the traffic increase, roads become more andmore noisy. Function of the traffic composition and theoutdoor propagation conditions, populations can be submitted to substantial noise level variations. Their prediction implies to model the mixed influence of ground andatmospheric conditions. In most cases, the ground profiles and composition are complex and the meteorological situations unstable. Results reported here deal witha calculation method based on a numerical approach relevant to simulate various situations which can be metoutdoors. For this, we used a well-adapted and accurate model based on the parabolic approximation. Solution are calculated through a Split-Step Pad methodwhich has already been validated [1] and which appeared to be reliable with respect to its obvious advantagesin terms of angular aperture, CPU time and its capability to consider the main phenomena: homogeneous andmixed grounds, acoustic barriers. We propose here anextension of the code to the case of a non flat ground.

PARABOLIC EQUATIONThe problem of the propagation above a non flat groundhas recently been studied by several acoustic researchers.A curved terrain version of the parabolic equation hasbeen adapted for acoustic propagation in the atmosphereover fairly simple terrain profiles which can be reducedto a set of joined circular section pieces [2]. In that approach, a separate conformal coordinate transformationwas applied to each circular section piece of atmosphere.Sack and West [3] chose to use a transformation whichfollows the terrain profile. Their method can be used forany smooth terrain but seems difficult to apply for a pa-

rabolic equation including wind terms. We chose to develop another model which can be used above any terrain and with a parabolic equation including wind terms[4]. The non flat ground is treated as a succession of flatdomains (see figure 1). After each flat domain the coordinate system is rotated so that the axis staysparallel to the ground. The calculation above each domain needs an initial solution. The values of the initialsolution for the domain are obtained from the values of the pressure field of the domain , except for thefirst domain where a gaussian starter is used. The proDomain 3Initial solutionDomain 1z

Domain 2

zr

zr

r

F IG . 1 Definition of the resolution domains.pagation code is based on the parabolic equation and aSplit-Step Pad method [5]. Introducing the envelope , !" , a marching algorithm is obtained:#

$&%'()+*-,

#

.0/1 2

$3(4+*-,

(1)

=F E , %4C:HGIF E and== , BC:D8where (56879 , *);: ?@[email protected]/1

of refraction. Equation 1 is then discretized by a finitedifference technique. Reflexions at the top of the numerical grid are controlled by introducing a thin artificialabsorption layer in the upper part of the computationdomain. The code has been tested in realistic outdoorconfigurations. The case of an impedance discontinuity

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RELATIVE SOUND PRESSURE LEVEL (20log(p/pref))

10SUCCESSION OF DOMAINSCONFORMAL MAPPING0

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510

601540

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20300

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100150DISTANCE (m)

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35dB

"! #$&% '&(')*,+.-

F IG . 3 Visualization of the relative sound pressure levelabove a wedge ().the wedge and more particularly diffraction phenomenaat the junctions between the flat domain are illustratedon figure 3.

CONCLUSIONWe have presented a new model for sound propagation above non flat ground .This model has been validated through a comparison with results obtained froma method using a conformal mapping. The next step ofour work is to integrate wind effects in the code by usinga new parabolic equation including wind terms [4]. Anoutdoor site near Saint Berthevin (France) has been selected to study the influence of meteorological conditions on noise traffic. Acoustical and meteorological measurements will be performed simultaneously. This survey will provide a database of noise level variations ina complex environment (non flat terrain, mixed ground)and thus allow us to validate our numerical simulationof outdoor sound propagation.

80

DISTANCE (m)

F IG . 2 Relative sound pressure levels versus range above aconvex cylinder.agreement between the two methods is very good. Othercomparisons have been carried out. The agreement isgood up to an angle of

radians between the flatdomains. Beyond this value, the approximation of thecylinder by flat domains gives rise to errors.

PROPAGATION ABOVE A WEDGEAn outdoor measurements campaign above a wedgeis planed as another benchmark case for our code. Weuse it to simulate the acoustic propagation above thewedge (figure 3). The height of the source is 2 m, thefrequency is 400 Hz. We use a finite impedance value torepresent a grassy ground. This value is calculated witha Delany and BazleyF model from an air flow resistivityvalue (200 ). The wedge has a slope of 10 deGgrees. The deformation of the acoustic field induced by

080ALTITUDE (m)

(infinite/finite) in a stratified atmosphere has been validated.The propagation above a cylinder is chosen as a benchmark case for our code. The calculation can be treated by a method using conformal mapping [2]. In thetransformed domain where the ground is flat, the effectof topography is accounted for by an effective soundspeed, which is exponentially increasing with height.For a convex cylinder, the sound speed profile used inthe transformed domain is given by 2

;is the radius of curvature and is a reference soundspeed. For the benchmark case the parameters of the calculation are a radius of curvature of 100 m, a sourceheight of 5 m and a frequency of 1000 Hz. The sound level is evaluated on a curved line at a height of 5 m abovethe cylinder. In our simulation the curved surface is splitted in 8 flat domains; the angle between two flat domainsisradians. On figure 2 we plot the relative soundpressure level

, where is the soundpressure in front of the source at a distance of 1 m. The

REFERENCES[1] P.Chevret, Ph. Blanc-Benon, and D.Juv. J. Acoust.Soc. Am., 100(6):35873599, 1994.[2] X. Di and K.E. Gilbert. The effect of turbulence andirregular terrain on outdoor sound propagation. InProc. 6th LRSP, pages 315333, NRC Ottawa Canada, 1994.[3] R.A. Sack and M. West. Applied Acoustics, 45:113129, 1995.[4] L. Dallois, Ph. Blanc-Benon, D. Juv, and V.E.Ostashev. A wide angle parabolic equation forsound waves in moving media. In Proc. 8th LRSP,pages 194208, State College, USA, 1998.[5] B. Gauvreau. Influence des conditions micromtorologiques sur lefficacit des crans acoustiques.PhD thesis, Universit du Maine, France, 1999.

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Calculation of noise barrier performance in athree-dimensional turbulent atmosphere using thesubstitute-sources methodJ. ForssnChalmers University of Technology, Department of Applied Acoustics, SE-412 96, Gteborg, Sweden.E-mail: [email protected] sources between a noise barrier and a receiver are used to calculate the effect of atmospheric turbulence on barrier soundreduction. The method is extended for application to three-dimensional situations with both high and low barriers. Calculations aremade for a thin, hard screen, without the influence of a ground surface. The Kirchhoff approximation is applied for the low screensand a more accurate diffraction model is used for the higher screens. The calculated results are compared with corresponding onesfor two-dimensional situations, also by using the substitute-sources method (SSM). The two and three-dimensional calculations givevery similar results, which indicates that only two-dimensional models are needed. The results are also compared with those obtainedusing a scattering cross-section method which, although it predicts a much weaker influence of turbulence than the SSM, shows thesame trend, namely that the turbulence influence is large only within a range of lower screen heights.

INTRODUCTIONThis paper describes an extension of the substitutesources method [1]. The problem under study is the increase in sound level behind barriers due to the influenceof atmospheric turbulence on the sound propagation.In terms of physical modelling, the problem can beseen as arising from two interacting processes: diffraction (due to the barrier) and sound propagation in an inhomogeneous medium. A direct numerical solution to thewhole problem would generally be very expensive computationally. The approach here is to describe the field ofa receiver, reached by sound from an original source, asa superposition of fields from a distribution of sources ona surface located between the original source and the receiver. The surface is denoted the substitute surface, andthe sources on it are substitute sources. (See Figure 1.)When the substitute surface is located between the barrier and the receiver, there is a free path from all of thesubstitute sources to the receiver, and the calculation ofthe sound propagation along the free path is possible for avariety of situations with an inhomogeneous atmosphere.A mutual coherence function for a turbulent atmospherehas been applied here (with the structure parameter Cv2describing the strength of velocity fluctuations). Anotherpossibility is to take into account the refraction due to asound speed profile.In this model the turbulent atmosphere is assumed toincrease the noise level behind the barrier by a decorrelation of the contributions from the substitute sources. Thisimplies that, in the absence of turbulence, the substitutesources must be interfering negatively.In a previous study [1], the Kirchhoff approximationwas used, which gives accurate results only for flat ge-

#

'"!

$&%

FIGURE 1. Geometrical situation with source, barrier, receiver,and the substitute surface, S.

ometries, i.e. when the barrier is low in comparison to itsdistance to the source and the receiver. The results werecompared with those from PE calculations. Here, calculations are made for 2-D and 3-D situations, both with andwithout the Kirchhoff approximation. The results fromusing the different approaches are compared; a comparison with a scattering cross-section method is also made.The situations studied here are without the influence of aground surface, for a thin hard screen with edge parallelto the z axis, and both the source and the receiver at z ( 0.The main parts of the theory are described in [1], anda full description is in a submitted paper [2], where alsomore numerical results are shown.

RESULTSCalculations with the diffraction accurately modelled,i.e. without the Kirchhoff approximation, were made forscreen heights H ( 2 ) 5 * 5 * 11 * 20 * 35 * and 50 m.

SESSIONS

b)

10

No turbulenceSSM 3-DSSM 2-DScattering Cross-sectionSSM 3-D KirchhoffSSM 2-D KirchhoffNo turbulence, 3-D KirchhoffNo turbulence, 2-D Kirchhoff

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Increase due to turbulence, dB

a)

Power relative to free field, dB

The maximum height needed for the substitute sourcesto give a good approximation of the field at the receiverpositions was obtained from test calculations. It wasfound that the height needed is much lower for calculations with turbulence than without. This means thatwhen the surface S is enlarged, the convergence is fasterwith turbulence than without, which is an interesting result and also leads to much shorter computation times.In the calculations for the homogeneous atmosphere, themaximum height needed to be approximately doubled. Adiscretisation distance of five points per wavelength wasused for all of the calculations.

0

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FIGURE 2. f5 m4 , 3 - s2 .+

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1000 Hz, dS+

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In Figure (2a) the dashed lines show the solutions fora homogeneous atmosphere using the Kirchhoff approximation. The 3-D and the 2-D results are very similarin these examples. They show unwanted oscillations atgreater screen heights that are caused by the finite accuracy in the numerical calculations, due to discretisationand the finite substitute surface, S. The solid lines arefor the turbulence introduced; the 3-D and 2-D results arevery similar.The results without the Kirchhoff approximation areplotted with symbols. The results are shown for 3-D and2-D calculations with turbulence, for those without turbulence, and for the scattering cross-section method calculations.In Figure (2b) the increase due to the turbulence isshown for the 3-D and the 2-D calculations, with andwithout the Kirchhoff approximation, as well as for thescattering cross-section method.The results show a higher sound level when atmospheric turbulence is introduced and in general it has beenshown that the effect of turbulence grows stronger whenthe frequency, screen to receiver distance, or turbulencestrength increases.

For the lower screen heights, the results with and without the Kirchhoff approximation show small differences,as expected. Above H . 5 m, however, they deviate significantly; using the Kirchhoff approximation is shownto lead to an underestimation of the sound level for thehomogeneous examples.Both the 3-D and the 2-D results, when not using theKirchhoff approximation, show that the influence of turbulence is weaker for the highest screens. Moreover, the3-D and 2-D results are very similar, which indicates thatthe sound level increase behind barriers, caused by atmospheric turbulence, can be predicted by using 2-D models.Although the scattering cross-section method predicts a much weaker influence of turbulence than thesubstitute-sources method (SSM), the results show thesame trend, namely that there is a range of lower screenheights for which the sound reduction is the most sensitive to turbulence. For the higher screens, where theturbulence influence is weak, the scattering cross-sectionresults tend to those for the SSM.For the higher screens, using the Kirchhoff approximation (outside its range of validity) shows an influenceof turbulence that is very weakly linked to the screenheight. This will not be the case if the Kolmogorovturbulence model used here is exchanged for a Gaussian model, resulting in a significant turbulence scatteringonly within a range of lower screen heights [3]. Probably,this contrast is caused by the fast decay with increasingwave number that the Gaussian model describes, sincethe smaller scales of the turbulence cause the large anglescattering.

ACKNOWLEDGMENTSThe author wishes to thank Wolfgang Kropp for inspiring discussions and critical reading. This work wasfinancially supported by MISTRA (the Swedish Foundation for Strategic Environmental Research).

REFERENCES1. Forssn, J. Acustica 86, 269275 (2000)2. Forssn, J. Calculation of noise barrier performance usingthe substitute-sources method for a three-dimensional turbulent atmosphere. Submitted to Acustica, April 20003. Forssn, J. Proc. 9th Int. Symp. on Long-Range SoundPropagation, The Hague, Netherlands, 1626 (2000)

SESSIONS

Recommendations for improvement of aircraft noisepropagation assessmentO. Zaporozhetsa, V. Tokareva, K. Attenboroughba

National Aviation University (NAU),1, Cosmonaut Komarov Prospect, Kyiv, Ukraine,03058bSchool of Engineering, University of Hull,Hull, HU6 7RX, UKHuge demands for more accurate and reliable methods of aircraft noise calculations provide the necessity to investigate particularelements of existing methods for aircraft noise calculations. Few national methods (USA, UK, Ukraine, Germany, Netherlands)and some international recommendations (ISO, ICAO, CAEC) are analysed and their poor elements are outlined. It was foundthat noise propagation assessment of the methods needs for improvements more necessarily. Thus theoretical and measurementanalysis of aircraft noise propagation are performed first of all. On their basis the improvements are proposed and the main ideais to implement the approach of routine generators for noise-power-distance-relationships (as a most important acousticcharacteristic of the aircraft to be calculated), for lateral attenuation and for screen effect assessment of the noise duringpropagation. Routine generators are the subprograms in a main aircraft noise calculation program and they must be supplied bynecessary current input data meteorological, flight and topographical.

INTRODUCTIONEnvironmental noise, caused by traffic, industrialand recreational activities is one of the main localenvironmental problems in Europe and the source of anincreasing number of complaints from the public. Forthis reason recent proposal on the review of the FifthAction Programme announces the development of anoise abatement programme for action to meet newtargets that is outlined in Green Paper and workinggroups were established for solving of the particulartasks. For example, harmonised calculation methodsand associated measurement methods shall be betterthan the present ISO or national models, shall beelaborated for noise from road, rail, and air traffic aswell as outdoor machinery and industry, for a varietyof geometrical and weather conditions, and they shouldbe valid for propagation over given distances (to beagreed) and have an agreed accuracy.The approach for total aircraft noise assessmentdescribed elsewhere [1]. Here the details on noisepropagation effects are outlined, as they wereinvestigated during last time.

GROUND EFFECT ASSESSMENT LATER-GENERATORAll relationships for the extra ground attenuation ofnoise Lint are based on approximate solutions for thereflection for spherical sound waves from locally

reacting plane surfaces. ISO 9613/2 proposesappropriate formulas for the ground effect calculationsfrom for two kinds of ground conditions withoutreference to source parameters. However it has beenfound that the differences between the predictedattenuation effects on overall A-weighted levels LA canas much as 12 dB as a result of spectrum variation,either for various types of aircraft (engines) under thesame conditions. The magnitude of the variation is thesame as for variance of Noise-Power-Distance (NPD)relationships LRn due to atmosphere conditionsobserved in operation. This means that not only thetype and mode of the engine, but also the influence ofambient conditions must be taken into account withequal accuracy and reliability. Differences between themagnitudes of lateral attenuation are considerable fordifferent types of reflecting surfaces also [2]. Dataobtained for grass surfaces have been used as the mostappropriate for calculations of noise levels around theairports (for environment impact assessment, forexample). Impedance characteristics can vary greatly.Sometimes mixed types of reflecting surfaces (insidethe aerodrome area) must be considered. It was foundthat the boundary between the coverings of varioustypes (for example inside aerodrome concrete-soil orconcrete-grass types of mixing are usual) behaves as aline of sound wave diffraction and the size ofdiffraction zone from discontinuity line is comparablewith length of sound wave [3]. All corrections havebeen obtained numerically with Chien and Sorokaapproach to interference effects and with a semiempirical model for impedance characteristics of

SESSIONS

reflecting surfaces. For routine aircraft noiseassessment a ground effect-generator has beenproposed (LATER-generator in Isobella soft tool,designed in Ukraine).

SCREEN EFFECTS ASSESSMENT SCREEN-GENERATORAny type of screens may be used for noiseabatement for ground modes of aircraft operations andmaintenance (engine run-ups) around the airports. Theeffects of screens are assessed by means of a modelwhich takes into account the effects of sounddiffraction at screen edges, interference of direct andreflected waves from various kinds of impedancesurfaces, each type of noise spectra generated by theaircraft, etc [2]. Spectral efficiencies of screens mustbe calculated for different kinds of noise propagation.Predictions of inserting loss in terms of OASPL (Lin)and LAmax (LA) for different types of noise sourcesunder identical conditions are shown in [2].The variation in the influence of the same type ofscreen on the results of noise abatement indicates theneed for screen affect assessment software for aircraftnoise calculations such as SCREEN-generator.

RECOMMENDATIONSRecommended procedures for ground attenuationassessment in aircraft noise calculations have beenproduced for several kinds of calculation schemes. Thestages in the procedure are outlined below:1.Calculation of acoustic spectrum at point ofnoise control:1.1.Calculation of the sound wave reflection fromfinite impedance surfaces1.1.1. General case (Chien/Soroka solution)1.1.2. Particular case: influence of the type of noisesource (monopole, dipole, quadrupole)1.1.3. Particular case: influence of discontinuity1.2. Assessment of the impedance characteristics ofthe surface2.Calculation of aircraft noise indexesperformed by means of generators for real noiseradiation spectrum:2.1.NPD-relationships are defined in a routinemode taking into account real ambient conditions, typeof the airplane with its known basic acoustic model (itsreal spectral characteristics) by use of RADIUSgenerator approach2.2.Generalized relationships may be used forassessment of the lateral attenuation for jet, fanjet or

propeller engines, but the approach of LATERgenerator is the most valid (for noise source with realnoise radiation spectrum)2.3.Generalized data may be used for assessmentof screen effects for jet, fanjet or propeller engines, butthe approach of SCREEN-generator is the most valid(for noise source with real noise radiation spectrum)

CONCLUSIONSFor best results of calculation of aircraft noisepropagation under the reflecting surfaces the followingfeatures must be taken into account: Assessment must be provided in a spectrumdomain (1/3-octave is preferable) and then the resultscan be recalculated in a form of noise indexes of anykind; Assessment provided for real noise sourcespectrum in accordance with engine type, mode anddirectivity pattern; Assessment accounts for dominant physical modelof elementary acoustic sources (monopole, dipole, etc)for the noise source under consideration (jet, fan,turbine, propeller, etc.); Assessment accounts for impedance characteristicsof the reflecting surfaces under consideration(homogeneous covering); Assessment accounts for discontinuity effect onlyin a case of near location of reflection point todiscontinuity line. At distances larger than one wavelength from discontinuity line the reflection effect islike to homogeneous covering only.

ACKNOWLEDGEMENTSNATO collaborative research grant EST.CLG 974767,1999

REFERENCES1. Zaporozhets O., Tokarev V. Aircraft noisemodelling for environmental assessment aroundairports // Applied Acoustics, Vol. 55, No. 2,1998, pp.99-127.2. Zaporozhets O., Tokarev V., Attenborough K..Improved calculation methods for assessing engine testnoise // Proceedings of the The InterNoise-2000, TheNice, France, 2000, August 27-30.3. Zaporozhets O., Tokarev V., Attenborough K. Basicrecommendations for assessing noise from groundsources at airports // Proceedings of The InterNoise2001, The Hague, The Netherlands,2001August 27-30.

SESSIONS

Application of two impedance discontinuity models toreal road traffic noise cases in inhomogeneous air conditionsJ. Defrance, E. PrematDepartment of Environmental Acoustics, CSTB24 rue Jospeh Fourier, 38400 St-Martin-dHres, Francecontact: [email protected] for road traffic noise are becoming more and more restrictive requiring the noise prediction to be achieved atranges where meteorological effects have to be taken into account. It is then of interest to evaluate the effect of the impedancediscontinuity at the edge of a road platform on noise propagation in inhomogeneous air conditions. This paper compares resultsobtained by two different models: a Boundary Element Method with an adapted Greens function and a modified Rasmussengeometrical method. Agreement between results from both of them is good. It appears from calculations that for a traffic noisesituation, the effect of the impedance discontinuity is sensible only when the celerity gradient becomes relatively high.

PRESENTATION OF THE MODELSzA first model presented in a twin paper [1] is aBoundary Element Method whose Greens function iscalculated analytically for the case of a positive linearcelerity gradient using the Normal Modessolution [2,3]. This method (called Meteo-BEM)shown to be powerful is taken as a reference here.The second model used for impedance discontinuityproblems is based on the well-known Rasmussen rayformulation [4] modified here in order to introduce thecelerity gradient effect [5]. The geometry of the such aproblem with a constant positive celerity gradient isgiven in Fig. 1 where the geometrical rays relative toone of the secondary sources Si above thediscontinuity are drawn in the case of singlereflections.

s1, 1SzS

1

s2, 2d1

s3, 3

z

Sizi

Rs4, 4

zR

2d2

FIGURE 1. Geometry of the discontinuity problemwith a constant positive celerity gradientFor quite small values of the constant gradient a0, it isknown that rays are circles with a radius of curvaturenearly equal to a0-1 . The analogy between flat ground+ curved rays ! circularly curved ground + straightrays can be applied giving a new problem of animpedance discontinuity on a concave surface inhomogeneous atmosphere (Fig. 2).

S

1

zS

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3

Si

zR

4

zi

d1

d2

FIGURE 2. Geometry of the discontinuity problemwith the curved ground analogyThe excess attenuation can be written as [4,5,6]: j 2 f ( 1 + 3 ) e+ s3 s1 s3 (s1 + s3 )0 ~ j 2 f ( 2 + 3 )~ j 2 f ( 1+ 4 )~ ~ j 2 f ( 2 + 4 ) Q1 eQ eQQ e+ 2+ 1 2 dz (1)s3 s 2 s3 (s 2 + s3 ) s4 s1 s4 (s1 + s4 ) s4 s2 s4 (s2 + s4 )

Att = 20 log

( d 1 + d 2 )d 2 8 k04

where f is the frequency, k0 is the wave number at z=0,si and i are the curvilinear length and travel time~~relative to the ith path (shown in Fig. 1). Q1 and Q2are the spherical wave reflection coefficientscalculated for paths 2 and 4 respectively, and correctedby an amplitude coefficient. This correction takes intoaccount the fact that the ray-tube area at Si (and R)associated to a reflected path on the curved surface islower than in the case of a flat ground with straightrays [6] inducing an increase of acoustical energy.Instead of calculating the exact values of si and i, weconsider that the two reflections shown in Fig. 2 occurat points I1 and I2 on tangential flat planes (see Fig. 3).

SESSIONS

z

~zR

~z i2

~z i1

10BEM HomGeom HomBEM InhomGeom Inhom

50

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I2

d1

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FIGURE 3. Geometry of the discontinuity problemwith the height correction principleThe problem is then similar to the Rasmussen one [4]with the following corrected heights [5]:

~zR = zR + zR ,zS = zS + zS , ~~~zi 1 = zi + zi 1 , zi 2 = zi + zi 22

(2)2

z d 2 z d2 z S = a0 S 1 , z R = a0 R 2 zS + zR 2 zS + zR 22

Excess Attenuation - dB

~zS

R

Si

S

The main limitation concerning the presence ofcaustics is being investigated as well as turbulence.

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(3)

RESULTS AND CONCLUSIONSSimulations have been carried out at 500 Hz with acelerity gradient of a0 = 2.9 10 3 m 1 making sourcereceiver distance vary. Geometry values arezS=zR=1 m and d1=20 m. Ground impedance iscalculated through the Delany and Bazleys oneparameter model with 1=300000 cgs and 2=300 cgs[1]. Results compared with Meteo-BEM simulationsare shown in Fig. 4a. Agreement is good.Another configuration representative of road trafficnoise has been studied at 500 Hz with a celeritygradient of a0 = 1 10 3 m 1 . Geometry values arezS=0.05 m, zR=2 m and d1=10 m, with 1=300000 cgs.The simulations have been achieved first with2=300 cgs (grass-like ground) then with 1=10 cgs(fresh snow). Comparisons in Fig. 4b show a quitegood agreement again.Same calculations could be carried out with negativegradients since this geometrical model is alsoapplicable to this situation, if out of the shadow zone.This method shall be applied to more complex celerityprofiles by considering equivalent linear gradientsdepending on frequency and geometry. It is alsopossible to adapt it to multi-reflections phenomenonoccurring in the case of a positive gradient situation.

Source-Receiver distance - mFIGURES 4a and 4b. Comparisons between modifiedRasmussen ray method (Geom, solid lines) andMeteo-BEM (BEM, dashed lines).(a) zS=zR=1 m, d1=20 m, 1=300000 cgs, 2=300 cgs,a 0 = 0 m 1 (thin lines) and a0 = 2.9 10 3 m 1 (thicklines).(b) zS=0.05 m, zR=2 m, d1=10 m, a 0 = 1 10 3 m 1 ,1=300000 cgs, 2=300 cgs (thin lines) and2=10 cgs (thick lines)

REFERENCES1. E. Premat, J. Defrance, Sound propagation above animpedance discontinuity in the presence ofmeteorological effects, using a BEM formulation, 17thICA, Roma, (2001)2. E. Premat, Y. Gabillet., A new boundary elementmethod for predicting outdoor sound propagation andapplication to the case of a sound barrier in the presenceof downwrad refraction, JASA 108(6), 2775-2783,(2000).3. E. Premat, Y. Gabillet and J. Defrance, Application ofthe Meteo-BEM model in downward and upwardrefraction conditions, 9th LRSP, The Hague, (2000).4. K.B. Rasmussen, A note on the calculation of thesound propagation over impedance jumps and screens,JSV 84(4), 598-602, (1982).5. J. Defrance and Y. Gabillet, A new analytical methodfor the calculation of outdoor noise propagation,Applied Acoustics 57, 109-127, (1999).6. A.D. Pierce, Acoustics. An introduction to its physicalprinciples and applications, McGraw-Hill Ed., (1981).

SESSIONS

Variation of the Characteristic Impedance in Air withEnvironmental ConditionsG. S. K. WongInstitute for National Measurement StandardsNational Research CouncilOttawa, Ontario, Canada, KIA 0R6With the demand for more precision in sound intensity and sound power measurements, it is necessary to calculate physicalparameters such as the Characteristic Impedance Dc (the product of density and sound speed) in air with less uncertainty. Withthe latest knowledge on the density and the velocity of sound in air, a method is described on the development of an empiricalequation for the computation of the variation of the characteristic impedance in air with temperature, humidity and barometricpressure.

INTRODUCTIONThe variation of Dc with humid air at sea level hadbeen investigated [1] with data usable from 0 to 30 oC.At a wider temperature range the computation of Dc canbe improved by dividing the process into two parts:sound speed and air density.

SOUND SPEED IN AIRWhen the barometric pressure changes from 90 to 110kPa, the sound speed in air, c (m/s), varies from theInternational Electrotechnical Commission (IEC)standard conditions of 23 oC, 101.325 kPa and 50 %RH, by approximately 50 ppm. This relatively smallvariation in sound speed due to barometric pressurechanges can be ignored in most acousticalmeasurements. However, sound speed is alsoinfluenced by temperature, humidity and carbondioxide content. For example, for an increase of 0.1 oC,the sound speed increases by approximately 0.058 m/sor 0.017 %; and an increase of 10 % RH at 23 oCincreases the sound speed by approximately 0.04 %.Similarly, an increase of CO2 concentration [2] by 1 %,the sound speed decreases by approximately 0.32 %.With the aim to have a low uncertainty in mind asimplified computation method [3] with knownuncertainty for sound speed as functions of temperaturet, humidity h and carbon dioxide content C in sea levelstandard air is used. The sound speed ratio c/c0 is:

where c0 is the sound speed for dry air, (331.29 m/s), at0 oC and at sea level, t is the temperature in Celsius; Cis the percentage carbon dioxide content, (assumed tobe 0.04 percent for standard air); h is the humidity with0 to 1 to represent RH from 0 to 100 %; and thenumerical constants [3] are:a0a1a2a3a4a5a6a7a8a9a10a11a12

=============

1.0001001.8286 x 10-3-1.6925 x 10-6-3.1066 x 10-3-7.9762 x 10-63.4000 x 10-98.9180 x 10-47.7893 x 10-51.3795 x 10-69.5330 x 10-81.2990 x 10-54.8016 x 10-5-1.4660 x 10-6

The sound speed at the above IEC referencecondition is 345.67 m/s. The uncertainty of the soundspeed computed with (1) is estimated at approximately450 ppm. from 0 to 50 oC.

THE DENSITY OF AIRThe basic equation for is given by Giacomo [3]:

2

c/c 0 = a 0 + a 1 t + a 2 t + a 3 C + a 4 C t

r=

2

+ a 5 Ct + a 6 h + a 7 h t + a 8 h t 23

2

2

+ a9ht + a10C + a11h + a12hCt

( pM a ) M v 1 - xv 1 (ZRT) M a

(1)

SESSIONS

(2)

where p, Ma , Mv, Z , psv , R, T, xv , xsv (= h.xsv)

, xsv (= h. fe. psv /p), and fe are the barometric

pressure, molar mass of dry air, molar mass of watervapour, compressibility factor, saturated vapourpressure, universal gas constant, kelvin temperature,mole fraction of water vapour in moist air, and insaturated moist air, and an enhancement factor tocompensate for gas imperfection, respectively.By applying the constants, such as R, Ma andcoefficients for the calculation of the compressibilityfactor Z, etc. given by Davis [5]; and calculate fe fromthe coefficients given by Greenspan [6] for water fortemperature from 0 to 100 oC; and compute psv bycurve fitting the data given by Wexler [7] for the sametemperature range, one can compute the density ofmoist air.By combining (1) and (2) above to give Dc and applycurve fitting Dc as functions of t, h, and p an empiricalequation is obtained:2

REFERENCES1.

Wong, G. S. K. "Characteristic impedance of humid air," J.Acoust. Soc. Am. 80(4), 1203-1204 (1986).

2.

Wong, G. S. K. "Speed of sound in standard air," J. Acoust.Soc. Am. 79(5), 1359-1366 (1986).

3.

Wong, G. S. K. "Approximate equations for some acousticaland thermodynamic properties of standard air," J. Acoust. Soc.Jpn. (E) 11, 145-155 (1990).

4.

Giacomo, P. Equation for the determination of the density ofmoist air (1981), Metrologia, 18, 33-40 (1982).

5.

Davis, R. S. Equation for the determination of the density ofmoist air (1981/91), Metrologia, 29, 67-70 (1992).

6.

Greenspan, L. Functional equations for the enhancementfactors for CO2-free moist air, NBS Journal of Research, Vol.80A, No. 1 January-February, 41-44 (1976).

7.

Wexler, A. Vapor pressure formulation for water in range 0 to100 oC. A revision, NBS Journal of Research, Vol. 80A, No. 5and 6, September December, 775-785 (1976).

2

Dc(t,p,h) = [a0 + (a1 + a2.h)p + (a3 + a4.h )p ] +2

2

[b0 + (b1 + b2.h)p + (b3 + b4.h )p ].t +2

2

2

[b0 + (c1 + c2.h)p + (c3 + c4.h )p ].t

(3)

where the coefficients a, b and c are constants.The uncertainty of (3) depends heavily on theuncertainty in the measurement of the parameters t, hand p. With modern measuring instruments, one mayassume the uncertainties of the measurement of theabove parameters as 0.1 oC, 5 % RH and 100 Pa,respectively. Over the temperature range from 0 to 50oC, barometric pressure from 90 to 110 kPa, andhumidity from 0 to 90 % (h from 0 to 0.9), the standarduncertainty for Dc calculated with the above procedureis estimated to be less than 0.2 % with a confidencelevel of approximately of 95 %.

CONCLUSIONSThe above is only an outline for the computationprocedure. With the aim for a lower uncertainty in thecomputation of the variation of Dc with theenvironment, work is continuing to arrive at theoptimum values for the constants shown in (3).

SESSIONS

An Efficient Method for the Prediction of SoundPropagation in a CanyonK. V. Horoshenkova, S. N. Chandler-Wildeb and D. C. Hothersallaa

Department of Civil and Environmental Engineering, University of Bradford, Bradford, BD7 1DP, UKb

Department of Mathematical Sciences, Brunel University, Uxbridge, UB8 3PH, UK

An efficient method is proposed to calculate the acoustic field in a canyon with two rigid walls and an impedance ground.In this method the infinite sum in the integral representation of the fundamental solution of the Helmholtz equation isreduced to a number of terms and the remainder, which are treated explicitly. A pole subtraction technique is used toensure smooth numerical integration of the derived functions. The developed expressions can be useful for efficient, 2-Dboundary element modelling of sound propagation in city streets with high-rise building facades of irregular shape.

INTRODUCTIONIn city street environments multiple reflections occur atthe building facades and the ground and can contributesubstantially to the overall sound levels. In outdooracoustics a two-dimensional version of the boundaryelement method (BEM) has been exploited to predictthe efficiency of road noise barriers [1] and the effect ofbuilding facades [2]. In principle, the BEM is notlimited by the extent of the acoustic region of interest,although specific programming implementation can berestricted by the size of the accessible computermemory and processor speed. In this paper it is shownthat the contributions from multiple reflections from theplane, rigid canyon walls can be incorporatedanalytically in the expression for the Green's function,which can be adopted in efficient BEMimplementations.

THEORETICAL FORMULATIONThe acoustic field at an arbitrary observation pointr = ( x, y ) from a line source at r0 = ( x0 , y 0 ) above animpedance boundary can be written as

G (r, r0 ) = G0 (r , r0 ) + P (r , r0 ) ,

(1)

where G0 (r, r0 ) is the 2-D Greens function for soundpropagation above a rigid boundary and P (r, r0 ) isthe perturbation term. The Greens functionG0 (r , r0 ) and the perturbation term P (r, r0 ) can beexpressed as Laplace-type integrals as [3]G 0 (r, r0 ) =

e i

0

cos( + w) + cos( w)v 2i2

e v dv2

(2)

and k is the wavenumber in air. Integrals (2) and(3) can be combined so that the Greens functionfor sound propagation above an impedanceboundary can be expressed asG (r, r0 ) =

2 eP (r , r0 ) =

0

thewhere isboundary = kx ,

cos(+ w) iw sin(+ w)

f (v 2 ) =

( 2 w2 ) v 2 2i

e

v

dv + Ps (3)

surface

impedanceofthe + = k ( y + y0 ) , = k ( y y0 ) ,

w = v v 2i , Ps is the surface wave term defined in [3]2

f (v

2

)e

v2

dv + Ps

(4)

0

w 2 {cos( + w) + cos( w)} 2iw sin( + w)( 2 w 2 ) v 2 2i

+

2 {cos( + w) cos( w)}

(5)

( 2 w 2 ) v 2 2i

The problem of multiple reflections from twoparallel rigid walls can be reduced to the problemof sound propagation from an infinite number ofperiodic sources elevated at the same heightabove the impedance ground. If the equivalentsources are at positions rl = ( x l , y 0 ) spaced withperiod 2h, then the resultant field at an arbitraryobservation point r = ( x, y ) is written as

G P (r, r0 ) = G (r, rl )

(6)

l =0

where l = 0, 1, ... and xl = x 0 + 2hl . The first Nterms can be extracted from sum (6) to be evaluatedexplicitly, using the efficient calculation methodproposed in [4]. Provided that x N > x , theremaining sum, from N+1 to infinity, can beexpressed as a single infinite integral using thegeometric series rule so thatGP (r, r0 ) =

2

where

andi

ei

N 1

Gl =0

where g (v 2 ) =

(r, rl ) +

e i N

g (v )e2

dv + Ps ( N ) (7)

0

f (v 2 )1 e

N v2

2 kh ( v 2 i )

, PsN is

the

surface

wave term and N = k ( x x0 + 2hN ) . Integral (7)can be calculated numerically using the Gauss-

SESSIONS

Laguerre quadrature rule. It can be shown that the demonstrated between the results of the twofunctiong (z ) canhavetwopoles, methods through the spectral range considered.

z a = i (1 1 2 ) and z b = i

CONCLUSIONSarg e i 2 khwhich can lie2khThe proposed calculation procedure is efficient as

close enough to the integration path to affect the accuracylong as k ( y + y 0 ) 2 / h is not too large. Unlikeof the numerical integration. It is suggested to subtractthese poles to overcome this problem. To subtract the the method of normal mode decomposition thepoles, the integral in exp. (7) can be presented in the form proposed method is robust when k y y 0 is

t 0.5e tdtt / N za ,b0

0.5 t 0.5 t g (t )t e dt = p(t )t e dt + a,b 0

0

(8)

a ,b

where t = N v 2 , p ( z ) = g ( z )

, a ,b = Res g ( z ) .z=zz z a ,bThe last term in exp. (8) is a table integral [5]. The polesubtraction ensures that the integrand p (t ) is boundedand analytic, as a function of t, in a neighbourhood ofthe positive real axis.

small. It is expected that the developed Greensfunction will prove useful in boundary elementmodelling of sound propagation in city streets andwaveguides and for problems of scattering byperiodic structures.

a ,b

REFERENCES1. Chandler-Wilde, S. N, "Tyndal medal lecture: Theboundary element method in outdoor noisepropagation," Proc. Institute of Acoustics, 19(8), 2750 (1997).2. Hothersall, D. C., Horoshenkov, K. V., Mercy, M.E., "Numerical modelling of the sound field near atall building with balconies near a road," J. SoundVib., 198, 507-515 (1996).3. Chandler-Wilde, S. N., "Ground effects inenvironmental sound propagation", PhD thesis,University of Bradford (1988).4. Chandler-Wilde, S. N. and Hothersall, D. C.,Efficient calculation of the Green function foracoustic propagation above a homogeneousimpedance plane, J. Sound Vib., 180, 705-724(1995)5. Abramowitz, M. and Stegun, I., Handbook ofMathematical Functions, Dover Publications, NewYork, 1964.6. Attenborough, K.Acoustical impedance models foroutdoor ground surfaces, J. Sound Vib., 99, 521-544(1985).7. Morse, P.M., Ingard, K.U., Theoretical Acoustics,Princeton University Press, Princeton, 1986.

Exp. (7) can now be used to construct the acoustic fielddue to an array of sources extending to infinity in bothdirections, i.e. G DP (r , r0 ) =

l =

G

l =

(r, rl ) . If we let

~xl = 2 x x l so that ~rl = ( ~xl , y 0 ) , then the periodicimpedance Greens function is written asG DP (r, r0 ) = G (r, r0 ) + G P (r, r0 ) + GP (r, ~r0 ) .

(9)

The solution to the problem of sound propagation froma point source at r0 in the canyon formed by twoparallel vertical walls emerging from an impedanceboundary can be given in terms of the periodic Greensfunction (9). The acoustic field in the canyon whichoccupies the strip 0 < x < h, y > 0 in the Oxy plane, hasrigid walls at x = 0 and x = h and an impedanceboundary condition on y = 0 is given by

G can (r, r0 ) = G DP (r, r0 ) + G DP (r, r0* ) ,

(10)

30

*

(

)

k G can (r, r0 ) in a city street canyon

Normal mode decomposition

100

L, dB

L = 20 log10

New method

20

where r0 are the images of rl in the wall at x = 0 .Exp. (10) was used to calculate the sound pressure level

-10

with a porous asphalt road surface. The positions of thesource and receiver were chosen to be at x 0 = 5.75 m,

-20

y 0 = 2.0 m, x = 1.5 m and y = 1.5 m. The width of the

-40

canyon was set to 17 m. The Attenborough model [6]was used to predict the surface acoustic impedance ofthe porous asphalt road surface. The following nonacoustic parameters were adopted in the model: flowresistivity R = 3500 Pa s m-2, porosity = 0.335,tortuosity q2 = 1.91, shape factor sp = 0.21, thickness d= 0.1 m. The result is shown in Figure 1, where it iscompared to that predicted by the method of normalmode decomposition [7]. Excellent agreement is

-50

-30

10

100

1000

10000

Frequency, Hz

Figure 1. Comparison of predictions using the proposedmethod and the method of normal mode decompositionfor sound propagation over a porous road surface.

SESSIONS

Acoustic Pulse Measurements over Mixed Impedance GroundProduced by a Snow CoverD. G. Albert, D. L. Carbee, F. E. Perron Jr., S. N. Decato and J. A. NagleU.S. Army ERDC-CRREL, 72 Lyme Road, Hanover, NH 03755 USABy selectively removing sectors of a natural snow cover, acoustic propagation paths with different lateral groundimpedance properties were produced. Measurements were then conducted over these paths to investigate the effect ofmixed ground impedance on acoustic waves. Blank pistol shots were used to produce the acoustic pulses that weredigitally recorded after propagating horizontal distances of 30 to 150 m. The first measurement was conducted over anundisturbed snow cover, a highly porous material with low acoustic impedance. Then, portions of the snow cover wereremoved and the measurements were repeated. Where the snow was removed, a less porous, higher impedance frozenground surface was introduced into the propagation path. The snow cover was removed in stages so that severaldifferent inhomogeneous ground impedance conditions were sampled, and a final measurement was made with thesnow cover entirely removed. Changes in the pulse waveforms were observed when only 10% of the propagation pathwas modified by plowing. Differences were also observed depending on whether the source was over snow or plowedground.

IntroductionThe interaction of sound energy with theground is an important factor in outdoor soundpropagation. Understanding this phenomenon isneeded for accurate noise propagationpredictions and for improved performance ofsensor systems. In realistic situations, andespecially in urban terrain, sound oftenencounters laterally varying ground, for examplegrass, paved, or snow-covered surfaces. Currentunderstanding of the effects caused by changingground properties along the propagation path islimited by a lack of experimental data, and onlysingle-frequency computational methods areavailable for predictions [15].

ApproachWe designed an experiment to investigate theeffect of lateral variations in ground impedanceon acoustic pulse propagation. By measuringpropagation across snow-covered ground, andsystematically removing areas of the snow coverby plowing, we were able to introduce largevariations in the ground impedance in acontrolled manner. Microphones were installedon the snow surface at three locations spaced 30m apart. Blank pistol shots were used as thesource of the waves. The pistol was held byhand 1 m above the snow or ground surface,pointed toward the sensors, and fired. Threedifferent source locations were used givingpropagation ranges between 30 and 150 m inlength. After shots were recorded from the threelocations, a swath of snow was removed by

plowing and the measurements were repeated.This procedure was followed until all of thesnow was removed. The signals from themicrophones were recorded using a digitalseismograph.

ResultsFigure 1 shows a few waveforms recorded overthe same 90-m path as sections of snow wereremoved. Visible changes in the recordedacoustic pulse are evident when only 10 m of thesnow was removed (11% of the path length).Generally, we measured different pulsewaveforms each time the ground conditions werechanged by plowing.Table 1. Waveform parameters from uniformimpedance model.EffectivePeakLabel Snow pressure uniformgroundinflow(Pa)Fig. 1 propagationresistivitydistance (m)(kRayls/m)A90 017B80 10213C60 30319D0 9021400In our first attempt to model thesemeasurements, we tested whether a uniformground impedance could be found to match theobserved data [6].This approach wassurprisingly- very successful, as can be seen bythe agreement with the dotted lines in the Figure.

SESSIONS

The ground impedance parameters determinedfrom the model are listed in Table 1.As the proportion of plowed ground increased,the effective air flow resistivity (s) needed tomatch the data increased from 7 kPa m2 (atypical snow value) to 400 kPa m2 (a typical bareground value). We found that the equation

Range = 90 mAB

Rsnowln (s ) 6 - 4Rsnow + Rgroundapproximately described the relationshipbetween the effective flow resistivity and theproportion of snow-covered ground in thepropagation path.Additional analysis of these data will bepresented in a future paper. These data provide arobust test set for the development of modelspredicting sound propagation above mixedimpedance ground.

AcknowledgementsWe thank Mr. Leon Stetson of North Pomfret,Vermont, for providing the field site. This workwas funded by the U.S. Army Corps ofEngineers.

References1.Boulanger, P., T. Waters-Fuller, K.Attenborough, and K.M. Lee, Models andmeasurements of sound propagation from a pointsource over mixed impedance ground, J. Acoust.Soc. Amer. 102, 14321442 (1997).2.Chandler-Wilde, S.N., and K.V.Horoshenkov, Pade approximations for theacoustical characteristics of rigid framed porousmedia, J. Acoust. Soc. Amer. 98, 11191129(1995).3. Daigle, G., J. Nicolas, and J.-L. Berry,Propagation of noise above ground having animpedance discontinuity, J. Acoust. Soc. Amer.77, 127135 (1985).4.Hothersall, D.C., and J.N.B. Harriott,Approximate models for sound propagationabove multi-impedance boundaries, J. Acoust.Soc. Amer. 97, 918926 (1995).5. Nyberg, C., The sound field from a pointsource above a striped impedance boundary, J.Acta Acoustica 3, 315322 (1995).6. Albert, D.G., Acoustic waveform inversionwith application to seasonal snow, J. Acoust.Soc. Amer. 109, 91-101 (2001).

CD0

2040Time, ms

60

Figure 1. Measured waveforms (solid lines) overa 90-m-long path as the snow was removed. (A)90 m snow (undisturbed). (B) 80 m snow, 10 mground. (C) 60 m snow, 30 m ground. (D) 90 mground. Dotted lines are theoretical predictionsusing a homogeneous ground impedance model.The waveform amplitudes are normalized.

SESSIONS

The Background Noise Level Analysis of Cultural CentersIn TaiwanH.R.Hsieha, R.P.Laib and Y.Y.Shiehca

Ph.D. Student, Dep. of Architecture, National Cheng-Kung University, Tainan, Taiwan, R.O.C.bProfessor, Dep. of Architecture, National Cheng-Kung University, Tainan, Taiwan, R.O.C.cLecturer, Dep. of Architectural Engineering, Kao Yuan Institute Technology, Kaohsiiung, Taiwan, R.O.C.The cultural center in Taiwan contains library, exhibition room and performance hall. While, the background noise level inthese three different areas are measured. According to the acceptable noise criteria. The unqualified rates are 86% for libraries,80% for exhibition rooms and 79% for performing halls. The major sources of noise all come from air-conditioning system. Inaddition, the managers of these areas and the performance groups are subjectively surveyed by questionnaires and it is found outthat the dissatisfied rate of the cultural centers background noise is around 17%-26%. Its very interesting and valuable forfurther investigation.

Cultural centers in Taiwan, which are open to generalpublic and relevant staff, serve as major places topromote cultural activities.It contain library,exhibition room and performing hall multipurposehall . This study is intended to discuss the backgroundnoise level in cultural centers. The aims of this studyare to objectively examine the real situation ofbackground noise level in cultural centers while airconditioning system are turned on, and to have asubjectively questionnaire to center managers andperforming groups in the aspect of background noiselevel.

ACCEPTABLE BACKGROUND NOISELEVEL CRITERIA IN CULTURALCENTERSRefer to C. M. Harriss 1979, [1] suggestion ofacceptable background noise level in concert hall andlarge auditorium is 30-35 dB (A), in library is 40-45dB (A). So we make a temporary acceptablebackground noise level criteria for performing hall is35 dB (A), for library is 45 dB (A). As to exhibitionroom, we consider as library, guilt chatter ispermissible, the acceptable background noise level is45 dB (A).

55 exhibition halls and 19 auditorium of performinghalls. We measured each rooms background noiselevel with turned on air-conditioning system and notednoise sources. Then we evaluated the results byacceptable temporary background noise level criteria.We also took a questionnaire to ask 23 cultural centermanagers and 507 performing groups include musicdance and drama groups about subjective noiseimpression. There were 23 valid questionnairesreceived from center managers and 87 validquestionnaires received from performing groups.

RESULTSThe results of background noise level with turned-onair-conditioning system in cultural centers are shown inFigure 1. The background noise impression of culturalcenter managers and performing groups is as present inFigure 2 and Figure 3.

dB(A)

INTRODUCTION

706050403020100

51.9

Reading areaareaofinReadinglibrarylibrary

51.3

Exhibition roomExhibitionroom

42.1

Acceptable level

Performing hallAuditoriumofperforming hall

METHODOLOGYThere are 23 cultural centers in Taiwan. The amountsof this study measured are 62 reading areas of libraries,

FIGURE 1. The average of background noise level withturned-on air-conditioning system in Taiwans cultural

SESSIONS

rooms or auditorium of performing halls, whichmajor background noise source came from airconditioning systems; the second was traffic noises.

centers.

ReadingareaareaofinReadinglibrarylibrary

ExhibitionroomExhibitionhall

Auditorium inAuditoriumofperforminghallperformingtheater100%

90%

noisy

80%

70%

fair

60%

50%

quietsilence

40%

30%

20%

10%

0%

veryquietquietsilence

very noisy

FIGURE 2. The impression of cultural center managersabout background no


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