Predicting sound absorption coefficients of lightweight multilayer curtains using the equivalent circuit method

A theoretical model to predict the sound absorption of lightweight multilayer curtains is presented. The fabric sheets of the curtain are represented by a network of discrete impedances describing the vibration and the airflow through the fabric. It is shown that the equivalent circuit method (EC) with correct modeling of the air cavities by distributed elements and the impedance transfer method (ITM) yield identical impedance relations. Formulas for the oblique incidence and the statistical absorption coefficient for curtains with an acoustically hard backing and without backing, i.e. freely hanging, are deduced. The model was validated by measurements on a set of 24 lightweight, woven fabrics. For the normal incidence absorption coefficient excellent agreement was achieved with mean value and standard deviation of the differences of 0.01±0.050.01±0.05. Based on the proposed model the following conclusions for the application of lightweight multilayer curtains can be drawn: (1) Sound-induced vibrations of the fabrics are an acoustically relevant aspect in the design of lightweight curtains. (2) The optimal specific airflow resistances of the individual layers may not be given in a compact analytical form but have to be determined by an optimization procedure. (3) The sound energy absorbed by curtains placed in the diffuse field of a room is in the same order of magnitude as the absorption by comparable curtains mounted in front of a wall. (4) For given mass and extension, multilayer arrangements perform superiorly to single layer curtains.