Measurements in the Reverberation Chamber
Authors: Sabine P. E. 
Published: September 2005

Our idea of the sound absorption coefficient of a surface is carried over from the optical analogy of the reflectivity of a surface for light. All reverberation theory and methods of measurement of absorption coefficients now extant are based on this conception of the dissipation of sound energy within a closed space. The fundamental assumptions underlying both theory and practice are as follows:
(a) That for the widely varying distribution of sound energy density that actually exists in the reverberant sound within a closed room we may substitute an average density which is the statistical mean of the distributed densities.
(b) That in place of the normal modes of vibration of a three-dimensional continuum we may substitute a diffuse distribution of energy flow within a room in which all directions of flow are equally probable.
(c) That the total sound energy which is incident upon different portions of the bounding surface during the course of the decay period is proportional to the respective areas of those portions independently of their respective absorptivities.
(d) That there exists for any material surface a single numerical coefficient of absorption for sound having the random distribution of incident angle assumed in a diffuse sound field and that the product of this coefficient and the area of the surface gives the contribution of that surface to the total equivalent absorption of any room in which the material in question forms a part of the exposed interior surface.
(e) That the geometry of the room and the distribution of absorbents in it are such that the idea of a “mean free path” of an element of a sound wave between reflections may be assumed to apply to the room as a whole.
Assumptions (a), (b) and (e) may reasonably be assumed to hold in reverberation chambers in which the conditions are such as to give a true logarithmic decay, the rate of which is constant independently of the position of the source, the microphone or the absorbent sample. Assumption (c) does not hold under the usual conditions of measurement of absorption coefficients in reverberation chambers, as witness the so-called “area effects” observed in all testing laboratories. It is highly probable that assumptions (a), (b) and (e) cannot properly be made under the conditions that usually exist in field measurements. They certainly do not in the case of large office spaces with extended ceiling treatment and in auditoriums with balconies and other recessed spaces. A diffuse distribution can hardly be assumed in large rooms with high absorption and correspondingly short decay periods.
The foregoing leads to the conclusion that as a general proposition assumption (d) is unwarranted. Hence, the job of the testing laboratories in the present state of knowledge is to find consistent numerical data by which absorbent materials may be rated as to their relative absorbing efficiencies. At present, wide differences appear in the results of measurements made in different laboratories on presumably identical materials with no means in sight for reconciling the discrepancies. However, published data on commercial absorbents from the National Bureau of Standards and the Riverbank Laboratories from measurements made in the last few years show on the average a close agreement in the values of the measured coefficients for frequencies between 512 and 2048 cycles. Fair agreement is shown at 256 cycles. At 128 cycles Riverbank values are consistently higher than National Bureau of Standards values for the same materials.
The results of a careful study of the errors of decay time measurements at 128 cycles as made in the Riverbank chamber are presented together with a critical analysis of the precision, in general, of absorption measurements by reverberation methods.
The author takes the position that in view of the statistical nature of the phenomena, and the inherently large variations in the computed coefficients resulting from slight variations in the experimental data, the state of our knowledge of the subject is not as hopeless as sometimes pictured. He urges the necessity of adequate testing facilities and equipment, and of ample experimental data.