A note on the acoustic insulation between two-dimensional acoustic spaces at low frequencies

The acoustic insulation provided by separating walls has been studied for many years, with the first publications dating from the early part of the 20th century [1]. Since then, different analytical and numerical models, for predicting the sound transmission via single and multi-panel walls, have been proposed. However, given the large number of variables of this problem and the uncertainties involved, laboratory tests have been devised to measure the insulation provided by separating elements. Among the various experimental testing methods, the most commonly used technique is the so-called two-room method [2–5]. It has been shown that, at low frequencies, the sound reduction index is highly dependent upon parameters such as the size of the testing chambers, sound source location and rooms’ surface absorption conditions [6–9], making it difficult to extrapolate test results to real-world situations. Indeed, the sound insulation provided by a wall is highly dependent on the vibration modes excited in the rooms, and on the vibration of the separating wall. The present work assesses the influence of the parallelism between the boundaries of the acoustic spaces and the importance of the rooms’ surface conditions on the characterization of the sound insulation offered by a wall separating two contiguous two-dimensional rooms. It makes use of a boundary element method (BEM) model, formulated in the frequency domain, previously developed by the authors [10], which takes into account the interaction, between the air and the solid walls. The acoustic insulation provided by walls of infinite extent is used as a reference (‘‘half-space room’’). These solutions are obtained analytically, taking also the full coupling between the air and the solid into account [11]. The formulation of the BEM method and the derivation of the analytical solution are not presented here, since they have been already given by the authors [10,11]. A survey of the state of the art more relevant to the present work can also be found in Santos et al. [10]. The remainder of