A war of coefficients or a meaningless wrangle over practical unessentials?

Paul E. Sabine was a distant cousin of Wallace C. Sabine. He continued Wallace's work at Riverbank Laboratories in Illinois after his cousin's death in 1919. His main focus was the development of Riverbank Labs into one of the leading testing institutions in the United States, even before “sound chambers” were built at the National Bureau of Standards (today NIST) and at universities. Paul's work focused on absorption coefficient measurements, and he published a series of articles on that topic.^1–6 He was strongly concerned with the precision of measurement of absorption coefficients by reverberation methods¹ and demonstrated the error of the measured value of the absorption coefficient when the reverberation time is not determined precisely. He was aware of the large variability of the measured absorption coefficient of the same sample in different laboratories. He investigated various source types (organ pipe and loudspeaker), and measured the reverberation time with the ear and stop watch method. Remarkably, the uncertainty with the ear and stop watch method was less than 1% when the reverberation times are compared from three different days (with 25 observations each). Sabine concluded from his investigations that the determination of the sound decay with a high precision is very important but remains difficult due to the logarithmic character of the decay curve and the fluctuating sound intensity due to the variation of the interference pattern in the reverberant sound. Finally, he noted that the interior treatment or the color in rooms would outweigh the uncertainties in the measured absorption coefficient values and that the so-called “war of coefficients” would be only a quite meaningless wrangle over practical unessentials in his opinion.

Since the pioneering work of W.C. Sabine and C.F. Eyring much progress has been made. In parallel and surely not independent from acoustic testing, the efficiency and variety of acoustic materials increased rapidly. Unfortunately, this also led to the “battle of the coefficients” due to the diversity in the acoustic values assigned to the same material measured in different laboratories.⁷ The Acoustical Society was founded in 1929 by four men, among them Paul E. Sabine, because of the “absorption coefficient problem.” At the 10th anniversary meeting of the Society the opening session was dedicated to exactly this ongoing problem. Sabine presented his collected findings from the viewpoint of the testing laboratory and remained positive that the problem could be solved in the future. In the following years important work was carried out: Maa⁸ derived the distribution of Eigentones for rectangular chambers and Hunt et al.⁹ analytically showed that modes have to be subdivided into groups having common properties. Kuttruff¹⁰ showed that the beginning of the sound decay contains the weighted mean of all decaying modes and should not be disregarded when calculating the reverberation time. Furthermore he showed that the sound decay is curved when plotted on a logarithmic axis and care has to be taken when defining “the” decay slope. Since Eyring's¹¹ contribution on the average sound absorption coefficient at least the battle of the coefficients is resolved and captured in international standards (ISO 354, ASTM C432) but the fighting against uncertainties still remains.¹² Recent developments which continue the ideas of former research^8–11 include the spatial decomposition of the (decaying) sound field,¹³ the isotropy of the incident sound field on the absorber,¹⁴ and the multi-exponential decay model for calculating decay times.¹⁵ In 2029 the 100th anniversary of the ASA will be celebrated with hopefully at least a partial solution to the “absorption coefficient problem.” Let us then open the time capsule from the 25th anniversary celebration¹⁶ and see if we satisfied the expectation of our famous pioneers in acoustics.

At the 10th anniversary meeting of ASA Paul E. Sabine⁵ concluded his presentation with the following statement: “The aim of architectural acoustics is a social one, directed toward the alleviation of the evil of noise and the enhancement of the enjoyment of speech and music. As long as our civilization moves towards social ends, architectural acoustics will continue an important branch of engineering science.” This presently can be regarded as one of the most important aims for acoustic engineers, namely, to design our surroundings to be a little bit more quiet and well-sounding.