Method for Calculating the Sound Absorption Coefficient for a Variable Range of Incidence Angles
Abstract
The theoretical estimation of sound absorption coefficient of a surface may give very different results. This will depend on the type of sound field assumed in the theoretical model used for the estimation of its sound absorption coefficient. Absorption coefficients for normal and diffuse sound fields are widely known, although they may be far from the absorption values given by an absorbing material when it is finally installed inside a room or enclosed space, where a sound field closer to a spherical wavefront is more likely to be found. This work presents a theoretical study, which is addressed at obtaining a mathematical expression to calculate the sound absorption coefficient for a variable range of incidence angles, called $α_s$. The presented method uses a circular sound field incidence as an approximation to a spherical incidence. The estimation of this coefficient $α_s$ is based on obtaining the incident and reflected sound fields for a surface located facing a lineal source. The advantage of this calculation method over others lies on its capability to give results for circular, normal and random wave incidence depending on the range of incidence angles considered in the calculation.Keywords:
sound absorbing material, sound absorption coefficient, circular wave incidence.References
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5. ISO 354:1985, Acoustics. Measurements of sound absorption in a reverberation room. 6. ISO 10534-1:1996, Acoustics. Determination of sound absorption coefficient and impedance in impedance tubes. Part 1: Method using standing wave ratio.
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12. Nocke C. (2000), In situ acoustic impedance measurement using a free-field transfer function method, Applied Acoustics, 59(3): 253–264, https://doi.org/10.1016/S0003-682X(99)00004-3.
13. O’Neil M., Greengard L., Pataki A. (2014), On the efficient representation of the half-space impedance Green’s function for the Helmholtz equation, Wave Motion, 51(1): 1–13, https://doi.org/10.1016/j.wavemoti.2013.04.012.
14. Pleban D. (2013), Method of testing of sound absorption properties of materials intended for ultrasonic noise protection, Archives of Acoustics, 38(2): 191–195.
15. Putra A., Khair F., Nor M. (2015), Utilizing hollow-structured bamboo as natural sound absorber, Archives of Acoustics, 40(4): 601–608, https://doi.org/10.1515/aoa-2015-0060.
16. Williams E.G. [Ed.], (1999), Fourier acoustics: Sound radiation and nearfield acoustical holography, Academic Press.
17. Yori A., Möser M. (2015), A measurement method for the sound absorption coefficient for arbitrary sound fields and surfaces, Acta Acustica united with Acustica, 101(4): 668–674, https://doi.org/10.3813/AAA.918862.
18. Yuzawa M. (1975), A method of obtaining the oblique incident sound absorption coefficient through an onthe- spot measurement, Applied Acoustics, 8(1): 27–41, https://doi.org/10.1016/0003-682X(75)90004-3.
2. Fahy F. [Ed.] (2001), Foundations of engineering acoustics, Academic Press. 3. Frisk G. (1979), Inhomogeneous waves and the plane-wave reflection coefficient, The Journal of the Acoustical Society of America, 66(1): 219–234, https://doi.org/10.1121/1.383074.
4. Garai M. (1993), Measurement of the soundabsorption coefficient in situ: The reflection method using periodic pseudo-random sequences of maximum length, Applied Acoustics, 39(1–2): 119–139, https://doi.org/10.1016/0003-682X(93)90032-2.
5. ISO 354:1985, Acoustics. Measurements of sound absorption in a reverberation room. 6. ISO 10534-1:1996, Acoustics. Determination of sound absorption coefficient and impedance in impedance tubes. Part 1: Method using standing wave ratio.
7. ISO 10534-2:1996, Acoustics. Determination of sound absorption coefficient and impedance in impedance tubes. Part 2: Transfer-function method.
8. Mikulski W. (2013), Determinig the ound absorbing coefficient of materials within the frequency range of 5000–50000 Hz in a test chamber of a volume of about 2 m3, Archives of Acoustics, 38(2): 177–183.
9. Mommertz E. (1995), Angle-dependent in situ measurement of reflection coefficients using a subtraction technique, Applied Acoustics, 46(3): 251–263, https://doi.org/10.1016/0003-682X(95)00027-7.
10. Möser M. [Ed.] (1988), Analyse und synthese akustischer spektren, Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo.
11. Möser M., Barros J. [Eds] (2009), Acoustic Engineering. Theory and Applications [in Spanish: Ingeniería Acústica, Teoría y Aplicaciones], 2nd ed., Springer, https://doi.org/10.1007/978-3-642-02544-0.
12. Nocke C. (2000), In situ acoustic impedance measurement using a free-field transfer function method, Applied Acoustics, 59(3): 253–264, https://doi.org/10.1016/S0003-682X(99)00004-3.
13. O’Neil M., Greengard L., Pataki A. (2014), On the efficient representation of the half-space impedance Green’s function for the Helmholtz equation, Wave Motion, 51(1): 1–13, https://doi.org/10.1016/j.wavemoti.2013.04.012.
14. Pleban D. (2013), Method of testing of sound absorption properties of materials intended for ultrasonic noise protection, Archives of Acoustics, 38(2): 191–195.
15. Putra A., Khair F., Nor M. (2015), Utilizing hollow-structured bamboo as natural sound absorber, Archives of Acoustics, 40(4): 601–608, https://doi.org/10.1515/aoa-2015-0060.
16. Williams E.G. [Ed.], (1999), Fourier acoustics: Sound radiation and nearfield acoustical holography, Academic Press.
17. Yori A., Möser M. (2015), A measurement method for the sound absorption coefficient for arbitrary sound fields and surfaces, Acta Acustica united with Acustica, 101(4): 668–674, https://doi.org/10.3813/AAA.918862.
18. Yuzawa M. (1975), A method of obtaining the oblique incident sound absorption coefficient through an onthe- spot measurement, Applied Acoustics, 8(1): 27–41, https://doi.org/10.1016/0003-682X(75)90004-3.
