Compressibility of air in fibrous materials

Abstract

The dynamic compressibility of air in fibrous materials has been computed for two assumed configurations of fibers which are close to the geometry of real fiber materials. Models with parallel cylinders placed in a regular square lattice and placed randomly are treated. For these models the compressibility is computed approximately from the diameter and mean distances between cylinders. This requires calculation of the air temperature, which is calculated for cylinders in a regular lattice by the Wigner-Seitz cell approximation. In the case of random placement, the calculation is done by a summation over thermal waves from all fibers, and by a self-consistent procedure. Figures of the compressibility in the frequency range 10-100 000 Hz, are given for diameter of the cylinders of 6.8 m, and mean distances between them from 50 to 110 m, which corresponds to glass wool with a density of 40 to 16 kg/m 3 . When the theoretical values for random placement were compared with measurements, it turned out that the random model could not describe the experimental data. However, they could be described accurately by assuming that the fibers have a tendency to form pairs.

Sound absorbing characteristics of fibrous metal materials at high temperatures

“…Dup'ere presented theories to calculate the surface dragging force, and the coupling between temperatures and density fluctuations had been taken into account by method of Lambert [21], and the calculation of the bulk modulus were not mentioned. Tarnow [10,11] considered that the cross-sections were irregular polygons due to parallel fibers 0003-682X/$ -see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.apacoust.2009.09.001 random arrangement.…”

“…Many authors [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] have studied the damping of acoustic waves by viscosity effect. Delany and Bazley [1] presented simple power-law relations obtained by best fitting a large amount of experimental data.…”

Measurements of anisotropic sound propagation in glass wool

“…͑4͒ with the time constant 0.50 ms, which was found from earlier measurements of the compressibility. 13 These measurements were done on glass wool samples with the same fiber diameters but a little higher density, 16 and 40 kg/m 3 , where the samples studied here have 14 and 30 kg/m 3 . Measurements of compressibility are very difficult, and the data are very scattered.…”

Fiber movements and sound attenuation in glass wool

“…͑A2͒ must be changed in the manner shown in an earlier paper by the author. 8 To obtain self-consistency, the value of K h computed by Eq. ͑A2͒ is set into Eq.…”

“…8 The effective heat capacity of fibers per volume is called K h . First set K h ϭ0, then compute the wave number of the heat wave in the air k h from…”