
doi: 10.1121/1.1902253
The relation between normal acoustic impedance and the various types of absorption coefficient has been discussed and specific formulas for the coefficients in terms of acoustic impedance have been published. Contours of constant absorption coefficient plotted as a function of the real and imaginary parts of acoustic impedance plotted on a linear scale are families of circles for both the normal coefficient, the coefficient which in the Sabine reverberation formula usually determines the initial rate of sound decay for rectangular chambers and low frequencies, and for the familiar free-wave absorption coefficient for any single angle of incidence. Similar contours for the Sabine or statistical absorption coefficient, which determines the rate of decay for completely diffuse sound, are shown to be very nearly circular. These plots, together with measured impedance curves or the equivalent electrical circuits of a sound-absorbing structure, are useful in designing materials and mountings for optimum sound-absorbing properties. The curves give theoretical explanation of the empirical value found by Sabine for the average cosine of the angle of incidence for frequencies above 500 c.p.s. Graphs of the absorption coefficients plotted as functions of magnitude of impedance for various values of impedance angle show that for angles greater than 45° the treatment of a complex impedance as a real impedance of the same magnitude introduces an error of greater than −20 percent in computing absorption coefficients.
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