A detailed analysis is carried out to clarify the mechanisms governing the acoustic performance of a permeable membrane and the effects of various material parameters. For this purpose, the theoretical solutions for the reflected and transmitted sound fields by an infinite permeable membrane which have been derived in a previous paper [J. Acoust. Soc. Am. 99, 3003-3009 (1996)] are approximated to obtain simple expressions for normal incidence absorption and transmission coefficients. An electrical circuit analogy is employed for a detailed analysis in which the particle velocity is separated into two components, i.e. the mass and the permeability, which is helpful in understanding their contributions to the acoustic properties of the permeable membrane. These considerations are aimed at demonstrating the effects of the parameters on the acoustic properties as well as explaining the following particular phenomena which are observed in the acoustic properties of a permeable membrane: the decrease of the sound energy absorbed in the structure at low frequencies and the increase of transmission loss at low frequencies due to the permeability. The optimal value of flow resistance for the most effective absorption is also obtained from those solutions. Detailed analysis of the acoustic properties of a permeable membrane

Membranes used for building materials have a certain degree of acoustic permeability, which has been disregarded in general membrane-vibration theory, and may cause serious effects especially on the acoustic properties. In this study, a theory for sound absorption of, and sound transmission through, a single permeable membrane is developed. Subsequently, sound absorption of structures composed of air layers, absorptive layers, and the facings of permeable membranes is investigated theoretically, and discussed in comparison with the experimental data measured by using the reverberation-room method. The results are in fairly good agreement; thus the present theory should give an effective tool for prediction of the acoustic properties of this type of membrane structure.

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A double-leaf microperforated panel space absorber (DLMPP) is composed of two microperforated panels (MPPs) placed in parallel with an air-cavity in-between, without a back wall or any backing structure. This was proposed as a space sound absorber, which can be used for a sound absorbing screen or partition. A conventional MPP absorber with a rigid back wall is effective only around its resonance frequency, which is usually at middle frequencies, and not effective at low frequencies. However, a DLMPP can be effective also at low frequencies, because an additional sound absorption is produced by its acoustic flow resistance. In the authors' previous work, theoretical analyses on the acoustic properties of a DLMPP were carried out using a simplified electro-acoustical equivalent circuit model. However, the equivalent circuit model includes an approximation, and more sophisticated theory is required for a better prediction and detailed discussion. In this paper, a revised theory for a DLMPP is presented: A Helmholtz integral formulation is employed to obtain a rigorous solution for more precise prediction of the absorptivity of a DLMPP. The result of the present revised theory is compared with that of the equivalent circuit model, and the difference between them is discussed. A parametric survey is made through numerical examples by the present revised theory to discuss its acoustic properties.

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