1、Designation: E 2611 09Standard Test Method forMeasurement of Normal Incidence Sound Transmission ofAcoustical Materials Based on the Transfer Matrix Method1This standard is issued under the fixed designation E 2611; the number immediately following the designation indicates the year oforiginal adopt
2、ion or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This test method covers the use of a tube, four micro-phones, and a digit
3、al frequency analysis system for themeasurement of normal incident transmission loss and otherimportant acoustic properties of materials by determination ofthe acoustic transfer matrix.1.2 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in this
4、standard.1.3 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Ref
5、erenced Documents2.1 ASTM Standards:2C 634 Terminology Relating to Building and Environmen-tal AcousticsE90 Test Method for Laboratory Measurement of AirborneSound Transmission Loss of Building Partitions and Ele-mentsE 1050 Test Method for Impedance and Absorption ofAcoustical Materials Using ATube
6、, Two Microphones andA Digital Frequency Analysis System2.2 ISO Standards:ISO 140-3 AcousticsMeasurement of Sound Insulation inBuildings and of Building ElementsPart 3: LaboratoryMeasurement of Airborne Sound Insulation of BuildingElements33. Terminology3.1 DefinitionsThe acoustical terminology used
7、 in this testmethod is intended to be consistent with the definitions inTerminology C 634.3.1.1 reference planean arbitrary section, perpendicularto the longitudinal axis of the tube that is used for the origin oflinear dimensions. Often it is the upstream (closest to the soundsource) face of the sp
8、ecimen but, when specimen surfaces areirregular, it may be any convenient plane near the specimen.3.1.2 sound transmission coeffcient, t(dimensionless) ofa material in a specified frequency band, the fraction ofairborne sound power incident on a material that is transmittedby the material and radiat
9、ed on the other side.t5WtWiwhere:Wtand Wi= the transmitted and incident sound power.3.1.3 sound transmission loss, TLof a material in aspecified frequency band, ten times the common logarithm ofthe reciprocal of the sound transmission coefficient. Thequantity so obtained is expressed in decibels.TL
10、5 10 log10SWiWtD5 10 log10S1tD3.1.3.1 DiscussionIn this standard the symbol TLnwill beapplied to sound which impinges at an angle normal to the testspecimen, as opposed to an arbitrary or random angle ofincidence.3.2 Symbols:c = speed of sound, m/s.r = density of air, kg/m3.f = frequency, hertz, (Hz
11、).G11, G22, etc. = auto power spectra (autospectrum) of theacoustic pressure signal at microphone locations 1, 2, and soon.G21, G32, etc. = cross power spectrum (cross spectrum) ofthe acoustic pressure signals at location 2 relative to location 1,3 relative to 1, and so on. In general, a complex val
12、ue.1This test method is under the jurisdiction ofASTM Committee E33 on Buildingand Environmental Acoustics and is the direct responsibility of SubcommitteeE33.03 on Sound Transmission.Current edition approved March 1, 2009. Published March 2009.2For referenced ASTM standards, visit the ASTM website,
13、 www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.3Available from American National Standards Institute (ANSI), 25 W. 43rd St.,4th Floor, New York, NY 10036, http:/ww
14、w.ansi.org.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.H21, H31, etc. = measured transfer function of the acousticpressure signals at location 2 relative to location 1, 3 relative to1, and so on. In general, a complex value. Note
15、 that H11ispurely real and equal to 1.HI, HII= calibration transfer functions for the microphonesin the standard and switched configurations, respectively. See8.4.Hc= complex microphone calibration factor accounting formicrophone response mismatch.H21, H31, etc. = transfer function of two microphone
16、 signalscorrected for microphone response mismatch. In general, acomplex value.NOTE 1In this context, the term “transfer function” refers to thecomplex ratio of the Fourier transform of two signals. The term “fre-quency response function” arises from more general linear system theory(1).4This test m
17、ethod shall retain the use of the former term. Users shouldbe aware that modern FFT analyzers might employ the latter terminology.j =1k =2pf/c; wave number in air, m-1.NOTE 2In general the wave number is complex where k=krjki. kris the real component, 2pf/c, and kiis the imaginary component of thewa
18、ve number, also referred to as the attenuation constant, nepers/m. Thisaccounts for the effects of viscous and thermal dissipation in theoscillatory, thermoviscous boundary layer that forms on the inner surfaceof the duct, (2). The wave number k of the propagating wave interior tothe material being
19、tested is generally different from that in air, and may becalculated in certain cases from the acoustic transfer matrix.d = thickness of the specimen in meters; see Fig. 4.11, 12 = distance in meters from the reference plane (testsample front face) to the center of the nearest microphone onthe upstr
20、eam and downstream side of the specimen; see Fig. 4.s1, s2 = center-to-center spacing in meters between micro-phone pairs on the upstream and downstream side of thespecimen; see Fig. 4.R = complex acoustic reflection coefficient.a = normal incidence sound absorption coefficient.TLn= normal incidence
21、 transmission loss.k = complex wavenumber of propagation in the material,m-1.Z = characteristic impedance of propagation in the material,rayls.3.3 Subscripts, Superscripts, and Other NotationThe fol-lowing symbols, which employ the variable X for illustrativepurposes, are used in Section 8:Xc = cali
22、bration.XI, XII = calibration quantities measured with microphonesplaced in the standard and switched configurations, respec-tively.X= measured quantity prior to correction for amplitude andphase mismatch.|X| = magnitude of a complex quantity.f = phase of a complex quantity in radians.Xi = imaginary
23、 part of a complex quantity.Xr = real part of a complex quantity.3.4 Summary of Complex ArithmeticThe quantities in thisstandard, especially the transfer function spectra, are complex-valued in general. The following may be useful in evaluatingthe defining equations:ejv5 cosv! 1 j sinv!A 1 jB! 3 C 1
24、 jD! 5 AC 1 BD! 1 jAD 1 BD!1/A 1 jB! 5 A / A21 B2! jB / A21 B2!4. Summary of Test Method4.1 This test method is similar to Test Method E 1050 in thatit also uses a tube with a sound source connected to one endand the test sample mounted in the tube. For transmission loss,four microphones, at two loc
25、ations on each side of the sample,are mounted so the diaphragms are flush with the inside surfaceof the tube perimeter. Plane waves are generated in the tubeusing a broadband signal from a noise source. The resultingstanding wave pattern is decomposed into forward- andbackward-traveling components b
26、y measuring sound pressuresimultaneously at the four locations and examining theirrelative amplitude and phase. The acoustic transfer matrix iscalculated from the pressure and particle velocity, or equiva-lently the acoustic impedance, of the traveling waves on eitherside of the specimen. The transm
27、ission loss, as well as severalother important acoustic properties of the material, includingthe normal incidence sound absorption coefficient, is extractedfrom the transfer matrix.5. Significance and Use5.1 There are several purposes of this test:5.1.1 For transmission loss: (a) to characterize the
28、 soundinsulation characteristics of materials in a less expensive andless time consuming approach than Test Method E90 andISO 140-3 (“reverberant room methods”), (b) to allow smallsamples tested when larger samples are impossible to constructor to transport, (c) to allow a rapid technique that does
29、notrequire an experienced professional to run.5.1.2 For transfer matrix: (a) to determine additional acous-tic properties of the material; (b) to allow calculation ofacoustic properties of built-up or composite materials by thecombination of their individual transfer matrices.5.2 There are significa
30、nt differences between this methodand that of the more traditional reverberant room method.Specifically, in this approach the sound impinges on thespecimen in a perpendicular direction (“normal incidence”)only, compared to the random incidence of traditional methods.Additionally, revereration room m
31、ethods specify certain mini-mum sizes for test specimens which may not be practical for allmaterials. At present the correlation, if any, between the twomethods is not known. Even though this method may notreplicate the reverberant room methods for measuring thetransmission loss of materials, it can
32、 provide comparison datafor small specimens, something that cannot be done in thereverberant room method. Normal incidence transmission lossmay also be useful in certain situations where the material isplaced within a small acoustical cavity close to a sound source,for example, a closely-fitted mach
33、ine enclosure or portableelectronic device.4The boldface numbers in parentheses refer to the list of references at the end ofthis standard.E26110925.3 Transmission loss is not only a property of a material,but is also strongly dependent on boundary conditions inherentin the method and details of the
34、 way the material is mounted.This must be considered in the interpretation of the resultsobtained by this test method.5.4 The quantities are measured as a function of frequencywith a resolution determined by the sampling rate, transformsize, and other parameters of a digital frequency analysissystem
35、. The usable frequency range depends on the diameter ofthe tube and the spacing between the microphone positions.Anextended frequency range may be obtained by using tubes withvarious diameters and microphone spacings.5.5 The application of materials into acoustical systemelements will probably not b
36、e similar to this test method andtherefore results obtained by this method may not correlatewith performance in-situ.6. Apparatus6.1 The apparatus is a set of two tubes of equal internal areathat can be connected to either end of a test sample holder. Thenumber of sets of tubes depends on the freque
37、ncy range to betested.Awider frequency range may require multiple measure-ments on a set of several tubes. At one end of one tube is aloudspeaker sound source. Microphone ports are mounted attwo locations along the wall of each tube. A two- or four-channel digital frequency analysis system, or a com
38、puter thatcan effectively do the same calculations, is used for dataacquisition and processing.6.2 Tube:6.2.1 ConstructionThe interior section of the tube may becircular or rectangular and shall have a constant cross-sectionaldimension from end-to-end. The tube shall be straight and itsinside surfac
39、e shall be smooth, nonporous, and free of dust, inorder to maintain low sound attenuation. The tube constructionshall be sufficiently massive so sound transmission through thetube wall is negligible compared with transmission though thesample. See Note 3. Compliant feet or mounts must be used toatte
40、nuate extraneous vibration entering the tube structure fromthe work surface.NOTE 3The tube can be constructed from materials including metal,plastic, concrete, or wood. It may be necessary to seal the interior wallswith a smooth coating in order to maintain low sound attenuation for planewaves.6.2.2
41、 Working Frequency RangeThe working frequencyrange is:fl, f , fu(1)where:f = operating frequency, Hz,fl= lower working frequency of the tube, Hz, andfu= upper working frequency of the tube, Hz.6.2.3 The lower frequency limit flis determined by thespacing of the microphones and the accuracy of the an
42、alysissystem. The microphone spacing shall be greater than onepercent of the wavelength corresponding to the lower fre-quency of interest.6.2.4 The upper frequency limit fudepends on the diameterof the tube, the microphone spacing, and the speed of sound.6.2.4.1 DiameterIn order to maintain plane wa
43、ve propa-gation, the upper frequency limit (5) is defined as follows:fu,Kcdor d ,Kcfu(2)where:fu= upper frequency limit, Hz,c = speed of sound in the tube, m/s,d = diameter of the tube, m, andK = 0.586.6.2.5 For rectangular tubes, d is defined as the largestsection dimension of the tube and K is def
44、ined as 0.500.Extreme aspect ratios greater than 2:1 or less than 1:2 shouldbe avoided. A square cross-section is recommended.6.2.6 Conduct the plane wave measurements within thesefrequency limits established by Eq 1 in order to avoidcross-modes that occur at higher frequencies, when the acous-tical
45、 wave length approaches the sectional dimension of thetube.6.2.7 LengthThe tube should be sufficiently long for planewaves to be fully developed before reaching the microphonesand test specimen. A minimum of three tube diameters must beallowed between sound source and the nearest microphone.The soun
46、d source may generate non-plane waves along withdesired plane waves. The non-plane waves usually will subsideat a distance equivalent to three tube diameters from thesource. If measurements are conducted over a wide frequencyrange, it may be desirable to use a tube, which providesmultiple microphone
47、 spacing, or to employ separate tubes. Theoverall tube length also must be chosen to satisfy the require-ments of 6.5.3 and 6.5.5.6.2.8 Tube TerminationThe termination of the tube isarbitrary in principle, but experience has found that the mostuseful termination is at least weakly anechoic, causing
48、minimalreflection of the sound wave back down the tube. A convenientway of providing this is to install a wedge or pyramidal shapedsection of some sound absorbing material such as glass fiber,about 30 cm long, in the open end of the tube. As the two-loadmethod requires a second measurement with a di
49、fferent tubetermimation, the wedge should be easily removable so that anopen or closed termination may be provided.6.2.9 Tube VentingSome tube designs cause large tempo-rary pressure variations to be generated during installation orremoval of the test specimen. This may induce microphonediaphragm deflection. By including a pressure relief opening ofsome type, the potential for damage to a microphone dia-phragm due to excessive deflection may be reduced. One wayto accomplish this is by drilling a small vent, 1 to 2 mm indiameter, through the wal
