1、Designation: E2611 09E2611 17Standard Test Method forMeasurement of Normal Incidence Sound Transmission ofAcoustical MaterialsDetermination of Porous MaterialAcoustical Properties Based on the Transfer Matrix Method1This standard is issued under the fixed designation E2611; the number immediately fo
2、llowing the designation indicates the year oforiginal adoption 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 meth
3、od covers the use of a tube, four microphones, and a digital frequency analysis system for the measurementof normal incident transmission loss and other important acoustic properties of materials by determination of the acoustic transfermatrix.1.2 The values stated in SI units are to be regarded as
4、standard. No other units of measurement are included in this standard.1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibilityof the user of this standard to establish appropriate safety and health practices and determine the
5、 applicability of regulatorylimitations prior to use.1.4 This international standard was developed in accordance with internationally recognized principles on standardizationestablished in the Decision on Principles for the Development of International Standards, Guides and Recommendations issuedby
6、the World Trade Organization Technical Barriers to Trade (TBT) Committee.2. Referenced Documents2.1 ASTM Standards:2C634 Terminology Relating to Building and Environmental AcousticsE90 Test Method for Laboratory Measurement of Airborne Sound Transmission Loss of Building Partitions and ElementsE1050
7、 Test Method for Impedance and Absorption of Acoustical Materials Using a Tube, Two Microphones and a DigitalFrequency Analysis System2.2 ISO Standards:ISO 140-3 AcousticsMeasurement of Sound Insulation in Buildings and of Building ElementsPart 3: LaboratoryMeasurement of Airborne Sound Insulation o
8、f Building Elements33. Terminology3.1 DefinitionsThe acoustical terminology used in this test method is intended to be consistent with the definitions inTerminology C634.3.1.1 reference planean arbitrary section, perpendicular to the longitudinal axis of the tube that is used for the origin of linea
9、rdimensions. Often it is the upstream (closest to the sound source) face of the specimen but, when specimen surfaces are irregular,it may be any convenient plane near the specimen.3.1.2 sound transmission coeffcient, (dimensionless) of a material in a specified frequency band, the fraction of airbor
10、nesound power incident on a material that is transmitted by the material and radiated on the other side.5WtWi1 This test method is under the jurisdiction of ASTM Committee E33 on Building and Environmental Acoustics and is the direct responsibility of Subcommittee E33.01on Sound Absorption.Current e
11、dition approved March 1, 2009April 1, 2017. Published March 2009July 2017. Originally approved in 2009. Last previous edition approved in 2009 asE2611 09. DOI: 10.1520/E2611-09.10.1520/E2611-17.2 For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Customer Service at se
12、rviceastm.org. For Annual Book of ASTM Standardsvolume information, refer to the standards Document Summary page on the ASTM website.3 Available from American National Standards Institute (ANSI), 25 W. 43rd St., 4th Floor, New York, NY 10036, http:/www.ansi.org.This document is not an ASTM standard
13、and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Becauseit may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases onl
14、y the current versionof the standard as published by ASTM is to be considered the official document.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1where:Wt and Wi = the transmitted and incident sound power.3.1.3 sound transmission lo
15、ss, TLof a material in a specified frequency band, ten times the common logarithm of thereciprocal of the sound transmission coefficient. The quantity so obtained is expressed in decibels.TL510 log10SWiWtD 510 log10S1D3.1.3.1 DiscussionIn this standard the symbol TLn will be applied to sound which i
16、mpinges at an angle normal to the test specimen, as opposed toan arbitrary or random angle of incidence.3.2 Symbols:c = speed of sound, m/s. = density of air, kg/m3.f = frequency, hertz, (Hz).G11, G22, etc. = auto power spectra (autospectrum) of the acoustic pressure signal at microphone locations 1
17、, 2, and so on.G21, G32, etc. = cross power spectrum (cross spectrum) of the acoustic pressure signals at location 2 relative to location 1, 3relative to 1, and so on. In general, a complex value.H21, H31, etc. = measured transfer function of the acoustic pressure signals at location 2 relative to l
18、ocation 1, 3 relative to 1,and so on. In general, a complex value. Note that H11 is purely real and equal to 1.HI,HII = calibration transfer functions for the microphones in the standard and switched configurations, respectively. See 8.4.Hc = complex microphone calibration factor accounting for micr
19、ophone response mismatch.H21, H31, etc. = transfer function of two microphone signals corrected for microphone response mismatch. In general, a complexvalue.NOTE 1In this context, the term “transfer function” refers to the complex ratio of the Fourier transform of two signals. The term “frequency re
20、sponsefunction” arises from more general linear system theory (1).4 This test method shall retain the use of the former term. Users should be aware that modernFFT analyzers might employ the latter terminology.4 The boldface numbers in parentheses refer to the list of references at the end of this st
21、andard.NOTE 1A, B, C, and D are the forward and backward components of the standing wave field. 1, 2, 3, and 4 are the measurement locations; 0 is anoptional reference location. Distances are measured from the specimen reference plane.FIG. 41 Schematic Drawing of the Measurement SetupE2611 172j = =2
22、1k = 2pif/c; wave number in air, m-1.NOTE 2In general the wave number is complex where k = kr jki.kr is the real component, 2pi f/c, and ki is the imaginary component of the wavenumber, also referred to as the attenuation constant, nepers/m. This accounts for the effects of viscous and thermal dissi
23、pation in the oscillatory,thermoviscous boundary layer that forms on the inner surface of the duct, (2). The wave number k of the propagating wave interior to the material beingtested is generally different from that in air, and may be calculated in certain cases from the acoustic transfer matrix.d
24、= thickness of the specimen in meters; see Fig. 1Fig. 411, 12 = distance in meters from the reference plane (test sample front face) to the center of the nearest microphone on theupstream and downstream side of the specimen; see Fig. 1Fig. 4s1, s2 = center-to-center 2 = center-to-center spacing in m
25、eters between microphone pairs on the upstream and downstreamside of the specimen; see Fig. 1Fig. 4R = complex acoustic reflection coefficient. = normal incidence sound absorption coefficient.TLn = normal incidence transmission loss.k = complex wavenumber of propagation in the material, m-1.Z = char
26、acteristic impedance of propagation in the material, rayls.3.3 Subscripts, Superscripts, and Other NotationThe following symbols, which employ the variable X for illustrativepurposes, are used in Section 8:Xc = calibration.XI,XII = calibration quantities measured with microphones placed in the stand
27、ard and switched configurations, respectively.X = measured quantity prior to correction for amplitude and phase mismatch.|X| = magnitude of a complex quantity. = phase of a complex quantity in radians.Xi = imaginary part of a complex quantity.Xr = real part of a complex quantity.3.4 Summary of Compl
28、ex ArithmeticThe quantities in this standard, especially the transfer function spectra, are complex-valued in general. The following may be useful in evaluating the defining equations:ej5 cos !1jsin!A1jB! 3C1jD! 5AC1BD!1jAD1BD!1/A1jB! 5A/A21B2!2jB/A21B2!4. Summary of Test Method4.1 This test method
29、is similar to Test Method E1050 in that it also uses a tube with a sound source connected to one end andthe test sample mounted in the tube. For transmission loss, four microphones, at two locations on each side of the sample, aremounted so the diaphragms are flush with the inside surface of the tub
30、e perimeter. Plane waves are generated in the tube usinga broadband signal from a noise source. The resulting standing wave pattern is decomposed into forward- and backward-travelingcomponents by measuring sound pressure simultaneously at the four locations and examining their relative amplitude and
31、 phase.The acoustic transfer matrix is calculated from the pressure and particle velocity, or equivalently the acoustic impedance, of thetraveling waves on either side of the specimen. The transmission loss, as well as several other important acoustic properties of thematerial, including the normal
32、incidence sound absorption coefficient, is extracted from 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 sound insulation characteristics of materials in a less expensive and less timeconsuming approach than
33、 Test Method E90 and ISO 140-3 (“reverberant room methods”), (b) to allow small samples tested whenlarger samples are impossible to construct or to transport, (c) to allow a rapid technique that does not require an experiencedprofessional to run.5.1.2 For transfer matrix: (a) to determine additional
34、 acoustic properties of the material; (b) to allow calculation of acousticproperties of built-up or composite materials by the combination of their individual transfer matrices.5.2 There are significant differences between this method and that of the more traditional reverberant room method. Specifi
35、cally,in this approach the sound impinges on the specimen in a perpendicular direction (“normal incidence”) only, compared to therandom incidence of traditional methods. Additionally, revereration room methods specify certain minimum sizes for testspecimens which may not be practical for all materia
36、ls. At present the correlation, if any, between the two methods is not known.Even though this method may not replicate the reverberant room methods for measuring the transmission loss of materials, it canprovide comparison data for small specimens, something that cannot be done in the reverberant ro
37、om method. Normal incidenceE2611 173transmission loss may also be useful in certain situations where the material is placed within a small acoustical cavity close to asound source, for example, a closely-fitted machine enclosure or portable electronic device.5.3 Transmission loss is not only a prope
38、rty of a material, but is also strongly dependent on boundary conditions inherent inthe method and details of the way the material is mounted. This must be considered in the interpretation of the results obtainedby this test method.5.4 The quantities are measured as a function of frequency with a re
39、solution determined by the sampling rate, transform size,and other parameters of a digital frequency analysis system. The usable frequency range depends on the diameter of the tube andthe spacing between the microphone positions. An extended frequency range may be obtained by using tubes with variou
40、sdiameters and microphone spacings.5.5 The application of materials into acoustical system elements will probably not be similar to this test method and thereforeresults obtained by this method may not correlate with performance in-situ.6. Apparatus6.1 The apparatus is a set of two tubes of equal in
41、ternal area that can be connected to either end of a test sample holder. Thenumber of sets of tubes depends on the frequency range to be tested.Awider frequency range may require multiple measurementson a set of several tubes. At one end of one tube is a loudspeaker sound source. Microphone ports ar
42、e mounted at two locationsalong the wall of each tube. A two- or four-channel digital frequency analysis system, or a computer that can effectively do thesame calculations, is used for data acquisition and processing.6.2 Tube:6.2.1 ConstructionThe interior section of the tube may be circular or rect
43、angular and shall have a constant cross-sectionaldimension from end-to-end. The tube shall be straight and its inside surface shall be smooth, nonporous, and free of dust, in orderto maintain low sound attenuation. The tube construction shall be sufficiently massive so sound transmission through the
44、 tube wallis negligible compared with transmission though the sample. See Note 3. Compliant feet or mounts must be used to attenuateextraneous vibration entering the tube structure from the work surface.NOTE 3The tube can be constructed from materials including metal, plastic, concrete, or wood. It
45、may be necessary to seal the interior walls witha smooth coating in order to maintain low sound attenuation for plane waves.6.2.2 Working Frequency RangeThe working frequency range is:fl,f,fu (1)where:f = operating frequency, Hz,fl = lower working frequency of the tube, Hz, andfu = upper working fre
46、quency of the tube, Hz.6.2.3 The lower frequency limit fl is determined by the spacing of the microphones and the accuracy of the analysis system. Themicrophone spacing shall be greater than one percent of the wavelength corresponding to the lower frequency of interest.6.2.4 The upper frequency limi
47、t fu depends on the diameter of the tube, the microphone spacing, and the speed of sound.6.2.4.1 DiameterIn order to maintain plane wave propagation, the upper frequency limit (3) is defined as follows:fu,Kcd or d,Kcfu(2)where:fu = upper frequency limit, Hz,c = speed of sound in the tube, m/s,d = di
48、ameter of the tube, m, andK = 0.586.6.2.5 For rectangular tubes, d is defined as the largest section dimension of the tube and K is defined as 0.500. Extreme aspectratios greater than 2:1 or less than 1:2 should be avoided. A square cross-section is recommended.6.2.6 Conduct the plane wave measureme
49、nts within these frequency limits established by Eq 1 in order to avoid cross-modesthat occur at higher frequencies, when the acoustical wave length approaches the sectional dimension of the tube.6.2.7 LengthThe tube should be sufficiently long for plane waves to be fully developed before reaching the microphones andtest specimen. A minimum of three tube diameters must be allowed between sound source and the nearest microphone. The soundsource may generate non-plane waves along with desired plane waves. The non-plane waves usually w
