In the first of a series of papers on the measurement of acoustical impedance of absorbing surfaces in-situ, the development of the theoretical methods for the determination of acoustic impedance by the two-microphone transfer function technique is outlined. Each method is based upon a model for propagation of sound above a plane. The impedance calculation models include an expression based on the Weyl-van der Pol equation for propagation over an impedance plane, an exact method based on specular reflection, and an approximate equation based upon specular reflection. The algorithm proposed by Vigran is also derived, and a plane wave model developed for comparison. Conditions under which the results from the different models are equivalent are discussed, along with the practical considerations in programming each model.
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References
1.
AllardJ.F.SiebenB. (1985). “Measurements of acoustic impedance in a free field with two microphones and a spectrum analyzer”, J. Acoust. Soc. Amer.77, 1617–1618.
2.
AllardJ.F.ChampouxY.NicolasJ. (1989). “Pressure variation above a layer of absorbing material and impedance measurement at oblique incidence and low frequencies”, J. Acous. Soc. Am.86, 766–770.
3.
American Society for Testing and Materials, ASTM 1977, 348–377, “Standard test method for impedance and absorption of acoustical materials by the tube method”. American Society for Testing and Materials, (1986). ASTM E1050. “Standard test method for impedance and absorption of acoustical materials using a tube, two microphones and a digital frequency analyzer system”.
4.
AttenboroughK. (1988). “Review of ground effects on outdoor sound propagation from continuous broadband sources”, Applied Acoustics24(4), 289–320.
5.
BS EN 20354: 1993. Measurement of sound absorption in a revereration room.
6.
ChampouxY.AllardJ.F.NicolasJ. (1988). “Measurement of acoustical impedance in a free field at low frequencies”, J. Sound Vib.125, 313–323.
7.
ChungJ.Y.BlaserD.A. (1980). “Transfer function method of measuring in-duct acoustic properties: I. Theory”, J. Acoust. Soc. Am.68, 907–913.
8.
ChungJ.Y.BlaserD.A. (1980). “Transfer function method of measuring in-duct acoustic properties: II. Experiment”. J. Acoust. Soc. Am.68, 913–921.
9.
CopsA.LauricksW. (1985). “Application of new two microphone techniques to measure sound absorption characteristics of acoustic materials”, 2nd International Congress onAcoustic Intensity, CENTIM, Senlis, France, 511–518.
10.
CramondA.J.DonC.G. (1984). “Reflection of impulses as a method of determining acoustic impedance”, J. Acoust. Soc. Am.75(2), 382–389.
HovemJ.M.IngramG.R. (1979). “Viscous attenuation of sound in saturated sand”, J. Acoust. Soc. Am.66, 1807–12.
13.
KinslerL.E.FreyA.R.CoppensA.B.SandersJ.V. (1982). “Fundamentals of Acoustics”, Third edition, John Wiley and Sons.
14.
MechelF.P. (1988). “Design charts for absorbing layers”, J. Acoust. Soc. Am.83(3), 1002–13.
15.
MLSSA, Maximum Length Sequence System Analyzer, DRA Laboratories, 1987.
16.
NobileM.A.HayekS.I. (1985). “Acoustic propagation over an impedance plane”, J. Acoust. Soc. Am.78(4), 1325–1336.
17.
OrlowskiR.J. (1981). “Measurement of the sound absorption coefficient of a factory roof at various angles of incidence”, Proceedings of the Institute of Acoustics12C3, 223–226.
18.
SeybertA.F.RossD.F. (1977). “Experimental determination of acoustic properties using a two-microphone random-excitation technique”, J. Acoust. Soc. Amen61, 1362–1370.
19.
SeybertA.F. (1988). “Two-sensor methods for the measurement of sound intensity and acoustic properties in ducts”, J. Acoust. Soc. Am.83, 2233–2239.
20.
VigranT.E.HoleS. (1988). “Sound absorbing layers: A simple prediction model for calculating absorption and the effect on sound transmission”, Proceedings of the Institute of Acoustics (U.K.)10(5), 31–38.
21.
VigranT.E. (1989). “Free field measurements of acoustical impedance: A simplified approach”, 13th International Conference on Acoustics, Yugoslavia.
22.
WaddingtonD.C. (1990). “Acoustical Impedance Measurement Using a Two-Microphone Transfer Function Technique”, PhD Thesis, University of Salford.
