Determination Of Diffuse Field Sound Absorption From A .
June 24, 2021Determination of Diffuse Field Sound Absorptionfrom a Normal Incidence Impedance MeasurementDavid HerrinUniversity of KentuckyUniversity of Kentucky
June 24, 2021Overview Normal and Diffuse Absorption Coefficient Normal Incidence Absorption – ASTM E1050 Diffuse Field Absorption – ASTM C423 Sample Size for ASTM C423 Diffusiveness in the Chamber Sensitivity StudiesThe Vibro-Acoustics Consortium2
June 24, 2021Normal Incident Absorption ASTM E1050Characteristic impedance𝑍𝐴𝑅𝐵Sound sourceReflection coefficient𝑅𝐵𝐴𝑍𝑍11Normal-incidence absorption𝛼1𝑅The Vibro-Acoustics Consortium3𝑖𝑋
June 24, 2021Normal Incidence Absorption VariationReconstituted Porous RubberReticulated FoamSolid line indicates the mean soundabsorption. Error bars indicate the 95%confidence limit in any one laboratorybased on round robin tests.Glass Fiber ASTM E1050 is very repeatable. 𝛼 is always less than 1.0.Cox and D’Antonio, 2017 adapted from Horoshenkov et al., 2007The Vibro-Acoustics Consortium4
June 24, 2021Diffuse Field Absorption ASTM C423Sound sourceMaterial of area 𝑆𝛼𝑉: Volume of reverberation room𝑉𝑑0.9210𝑐𝑆𝑐: speed of sound𝑑: decay rate, dB/sThe Vibro-Acoustics Consortium5
June 24, 2021Diffuse Field Absorption𝑇𝑆𝑆𝛼𝑚𝑉55.3𝑉𝑐 𝛼 𝑆𝑆𝛼 𝑆4𝑉𝑚Sample areaRoom surface areaAverage absorption coefficient of empty roomAir attenuationVolumeAbsorbing materialof area 𝑆Broadband sourceThe Vibro-Acoustics Consortium6
June 24, 2021Diffuse Field Absorption Variation100 mm mineral woolSolid line indicates the mean soundabsorption. Error bars indicate the 95%confidence limit in any one laboratorymeasurement on round robin tests (13laboratories). ASTM C423 is not as repeatablefrom to room to room. May exceed 1.0.25 mm foamCox and D’Antonio, 2017 adapted from Horoshenkov et al., 2007The Vibro-Acoustics Consortium7
June 24, 2021Absorption Greater than 1.0For a grazing wave, sound power is absorbedbut there is technically no “incident power”.The absorbed power increases when thesample has a finite size.The Vibro-Acoustics Consortium8
June 24, 2021ASTM C423Section 5.3 Diffraction effects usually cause the apparent area of a specimento be greater than its geometrical area, thereby increasing the coefficientsmeasured according to this test method. When the test specimen is highlyabsorptive, these values may exceed unity.Section 5.4 Regardless of the differences and the necessity for judgment,coefficients measured by the test method have been used successfully byarchitects and consultants in the acoustical design of architectural spaces.The Vibro-Acoustics Consortium9
June 24, 2021Sauro, 2010Discrepancy Edge Effect𝛼The Vibro-Acoustics Consortium10𝛼𝛽𝐸𝐸ratio of edges to area ofsample𝛼random incidence absorptioncoefficient of infinitely largesample (E 0)𝛽constant that depends onfrequency, the absorption,and the room.
June 24, 2021Heller, 2013Reverberation RoomWallace Sabine at Harvard UniversityThe Vibro-Acoustics Consortium11
June 24, 2021Discrepancy Between5 cm thick mineral wool(2.4 m x 2.4 m sample)𝜃1.2𝛼 𝜃14𝑅 cos 𝜃𝑅 cos 𝜃𝑋 cos 𝜃Average for diffusive incidence:Absorption10.80.6Normal Incident Absorption0.4Averaged for Infinite Panel0.2ASTM C4230𝛼2𝛼 𝜃 sin 𝜃 cos 𝜃 𝑑𝜃The Vibro-Acoustics Consortium100121000Frequency (Hz)
June 24, 2021Overview Normal and Diffuse Absorption Coefficient ASTM E1050 ASTM C423 Sample Size for ASTM C423 Diffusiveness in the Chamber Sensitivity StudiesThe Vibro-Acoustics Consortium13
June 24, 2021Thomasson, 1980Radiation Impedance𝑧Integral on area 𝑆 :𝑝𝑝 𝑥, 𝑦, 0𝑥, 𝑦𝑦𝑅𝑍𝑍2𝑝 𝑥, 𝑦, 0𝑍 : Radiation Impedance𝑆𝑥 ,𝑦𝑥𝑍𝑍 is a function of the geometry of theabsorber, frequency, and angle of incidence.𝑍2𝑝 𝑝𝑍The Vibro-Acoustics Consortium14
June 24, 2021Radiation Impedance𝑧 Incident waveAssuming a diffusive field𝜃/𝛼𝜑8 Re 𝑍𝑦𝑥sin 𝜃𝑑𝜃𝑍𝑍ZR of rectangular sample (2.44 m x 2.74 m)ZR𝜃0𝜃𝜋/6 𝜃𝜋/2𝑓63 Hz0.27 0.55i0.27 0.55i 0.24 0.52i𝑓125 Hz0.79 0.65i0.77 0.66i 0.51 0.68i 1.00 0.01i1.04 0.02i 3.37 3.41i 𝑓4000 HzThe Vibro-Acoustics Consortium15
June 24, 2021Size Correction1.65 cm mineral wool sample𝑒Diffuse Field Absorption1.4𝑒1.210.8e 3.6 m Measuremente 3.6 m Predictione 2.4 m Measuremente 2.4 m Predictione 1.2 m Measuremente 1.2 m PredictionNormal Absorption0.60.40.201001000Frequency (Hz)The Vibro-Acoustics Consortium16
June 24, 2021Overview Normal and Diffuse Absorption Coefficient ASTM E1050 ASTM C423 Sample Size for ASTM C423 Diffusiveness in the Chamber Sensitivity StudiesThe Vibro-Acoustics Consortium17
June 24, 2021Diffuse FieldRedstone Arsenal – U.S. ArmyTechnical University of DenmarkDiffuse Field means Sound pressure is uniform inside reverberation chamber Sound intensity distribution is uniform over all possibledirectionsThe Vibro-Acoustics Consortium18
Jeong, 2010Kang, 2000June 24, 2021Sound Intensity Distribution𝑧 Incident wave𝜃𝜑𝑦𝑥: Point source: Observation point𝜃: Incident angle𝜑: Azimuthal angleSimulation method by Jeong (2010) used beam tracing method.The Vibro-Acoustics Consortium19
June 24, 2021Sound Intensity DistributionIrregular roomNormalized intensityNormalized intensityRectangular roomIncident angle 𝜃Incident angle 𝜃The high frequency intensity is nearly independent of the room geometry, the locationof the absorber and the absorption coefficient of the specimen. – Jeong, 2010The Vibro-Acoustics Consortium20
June 24, 2021Jeong, 2010Intensity Distribution Correction1.215 cm mineral wool sample𝑒Absorption0.80.6Normal Incident Absorption0.4ASTM C423𝑒Size Corrected𝑒2.4 m0.2Size and Angle Corrected for Irregular RoomSize and Angle Corrected for Rectangular Room01001000Frequency (Hz)The Vibro-Acoustics Consortium21
June 24, 2021Overview Normal and Diffuse Absorption Coefficient ASTM E1050 ASTM C423 Sample Size for ASTM C423 Diffusiveness in the Chamber Sensitivity StudiesThe Vibro-Acoustics Consortium22
June 24, 2021ProcedureNormal Incidence Impedance1. Input layered sound absorber properties(thickness, flow resistivity, etc.).Diffuse Field Absorption2. Use empirical models and transfer matrixtheory to determine normal incidenceimpedance (𝑍 ) and normal incidencesound absorption (𝛼 ) in 1/6 octave bands.Sound source3. Use normal incidence impedance andsample size to determine diffuse field soundabsorption (𝛼 ).Material of area SThe Vibro-Acoustics Consortium23
June 24, 2021Normal Incidence vs. Diffuse Field1.4Absorption Coefficient1.210 cm (4 in) plastic foam1𝜎0.80.60.4Normal IncidenceDiffuse Field0.201001000Frequency (Hz)The Vibro-Acoustics Consortium245000 Rayls/m
June 24, 2021ASTM C423 Effect of Sample Size10 cm (4 in) plastic foam𝜎21.81.6Absoprtion CoefficientASTM C423 6.69 m2 (72 ft2) is recommended. Sample size 2.44 m2.74 m (8 ft 9 ft). Area may not be less than 5.57 m2(60 ft2).20,000 Rayls/m1.41.211.2 m X 1.1 m2.3 m X 2.3 m2.4 m X 2.4 m2.5 m X 2.5 m2.6 m X 2.6 m3.5 m X 3.5 m0.80.60.40.20100The Vibro-Acoustics Consortium251000Frequency (Hz)
June 24, 2021ASTM C423 Effect of Flow Resistivity1.61.410 cm (4 in) plastic foamAbsorption Coefficient1.210.80.65000 rayls/m0.410000 rayls/m20000 rayls/m0.230000 rayls/m01001000Frequency (Hz)The Vibro-Acoustics Consortium26
June 24, 2021ASTM C423 Effect of Mass Layer1Foil FoamFoam Thickness: 2.54 cm (1 inch)Foam Flow Resistivity: 30000 rayls/mFoil Surface Density: 0.05 kg/m2Absorption Coefficient0.80.60.4Foam (Normal Incidence)0.2Foam (Diffuse Field)Foil Foam (Normal Incidence)Foil Foam (Diffuse Field)01001000Frequency (Hz)The Vibro-Acoustics Consortium27
June 24, 2021References ASTM C423-09a, 2009, Standard Test Method for Sound Absorption and Sound AbsorptionCoefficients by the Reverberation Room Method. ASTM E1050-12, 2012, Standard Test Method for Impedance and Absorption of AcousticalMaterial Using a Tube, Two Microphones and a Digital Frequency Analysis System. Thomasson, S. I. (1980). On the Absorption Coefficient. Acta Acustica, 44(4), 265-273. Thomasson, S. I. (1982). Theory and Experiments on the Sound Absorption as Function of theArea. Report No. TRITA-TAK 8201, Department of Technical Acoustics, KTH, Stockholm,Sweden. Jeong, C. H. (2010). Non-Uniform Sound Intensity Distributions when Measuring AbsorptionCoefficients in Reverberation Chambers using a Phased Beam Tracing. The Journal of theAcoustical Society of America, 127(6), 3560-3568. Kang, H. J., Ih, J. G., Kim, J. S., and Kim, H. S. (2000). Prediction of Sound Transmission Lossthrough Multilayered Panels by using Gaussian Distribution of Directional Incident Energy. TheJournal of the Acoustical Society of America,107(3), 1413-1420.The Vibro-Acoustics Consortium28
ASTM C423-09a, 2009, Standard Test Method for Sound Absorption and Sound Absorption Coefficients by the Reverberation Room Method. ASTM E1050-12, 2012, Standard Test Method for Impedance and Absorption of
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