Original article Sound absorption modeling of thin woven fabrics backed by an air cavity Reto Pieren Abstract A theoretical model for the oblique incidence sound absorption coefficient of thin woven fabrics backed by an air cavity is presented where the fabric is acoustically described by its specific airflow resistance and its surface mass density. The theoretical model is illustrated by an equivalent electrical circuit and validated in the case of normal sound incidence by experimental results obtained from impedance tube measurements on three fabric types. The influence of the surface mass density on the absorption coefficient is discussed and recommendations for practical applications are derived. Further, a simple formula to predict the specific airflow resistance of woven fabrics based on geometrical parameters is deduced. The normal incidence absorption coefficient and geometrical parameters of a set of 24 fabrics with a large range of interyarn porosities and specific airflow resistances were measured and used to validate the proposed geo- metry-based model to predict the absorption coefficient. Measured and estimated absorption coefficients show excellent agreement, with mean value and standard deviation of the differences of 0.03  0.10. The model is therefore suitable for the design of new fabrics with an intended absorption coefficient. Keywords equivalent electrical circuit, sound absorption coefficient, specific airflow resistance, woven fabric In room acoustics, sound absorbers play a central role. In practical applications often textiles are employed as sound absorbers, for example, textile interior parts of automobiles or carpets in rooms that are used to absorb sound energy. 1 In these applications the absorbing material is mounted directly onto an acoustical hard surface. The textile can then be regarded as a porous medium and its sound absorption characteristic highly depends on its thickness. 2–4 However, when using curtains an air gap between the textile and the hard wall exists. Under these condi- tions also very thin textiles can have comparatively high sound absorption coefficients. 5,6 The application of cur- tains as sound absorbers for room acoustical purposes has several substantial advantages: curtains are rela- tively cost effective, lightweight, flexible, easy to manage and they enable variable room acoustics. Already in 1970 it was reported that the sound absorption of curtains depends on the mounting dis- tance to the wall, the airflow resistance and the surface mass density of the fabric, as well as the draping. 7 Today, common models to predict the absorption coef- ficient of curtains typically include the size of the air cavity and the specific airflow resistance of the fabric. 8,9 They assume that no sound-induced vibrations of the fabric occur, that is, the surface mass density of the fabric is high. However, several authors 10,11 proposed how to consider sound-induced vibrations in a mathe- matical model, but it was neither validated by measure- ments nor profoundly discussed. In 1990 it was phenomenologically shown that the intrinsic parame- ters of a textile, that is, its microstructure, has a sub- stantial influence on the sound absorption coefficient. 12 In 1999 this finding was emphasized by the use of an established mathematical model for micro-perforated panel (MPP) absorbers, 13,14 which was applied to thin woven textiles. 10 This model based on geometrical Empa, Swiss Federal Laboratories for Materials Science and Technology, Duebendorf, Switzerland. Corresponding author: Reto Pieren, Empa, Swiss Federal Laboratories for Materials Science and Technology, Ueberlandstr. 129, Duebendorf, 8600, Switzerland Email: reto.pieren@empa.ch Textile Research Journal 82(9) 864–874 ! The Author(s) 2012 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0040517511429604 trj.sagepub.com at Lib4RI on April 18, 2012 trj.sagepub.com Downloaded from