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Thermal Time Constants and Dynamic Compressibility of Air in Fiber-Filled Loudspeaker Enclosures
In a loudspeaker enclosure filled with fibrous damping material, the conduction of heat between the fibers and the air involves a time constant whose value depends on what conditions are held constant during the heat transfer. Five combinations of conditions are considered, leading to five different time constants. One of these, denoted by tfp, is the time constant at constant fiber temperature and constant pressure. Equations expressing the other four time constants in terms of tfp are derived using a thermal circuit model. Another thermal circuit yields an approximate analytical expression for tfp in terms of the diameter and packing density of the fibers and the thermal diffusivity of air. A more accurate numerical computation of tfp, based on separation of variables, is also obtained. By adjusting a single parameter in the analytical approximation, the approximation is made to agree with the numerical solution within a tolerance of ±2% for all possible input data. Assuming an intuitive form for the equivalent circuit of the acoustic compliance of the enclosure, it is shown that two of the five time constants can be read from the acoustic circuit, and hence that the components in the acoustic circuit can be calculated simply and accurately from the known properties of the enclosure and the filling.
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