In the past two articles on reverberation theory, we've focused on formulas and presented rather dry topics. So this time, I'd like to lighten the tone a bit and introduce the origins of Sabine 's formula, not from a theoretical standpoint, but from the experimental approach used to formalize the concept of reverberation time at the time.
While there is another equation for reverberation time besides Sabine 's, Eyring 's equation, which is more rigorous, Sabine 's equation is used in standards for acoustic measurement of materials in reverberation rooms, such as for sound insulation and sound absorption. This is because it has the advantage of being expressed in a simple formula using only three parameters: room volume, room surface area, and average sound absorption coefficient, in addition to the constant "K". Now, as the name suggests, Sabine 's equation was derived by Sabine, but not from the theory we have discussed so far. Sabine discovered through experiments that these three parameters are attributable to the length of sound reverberation in a room.
In 1895, a new art museum (Fogg Art Museum) opened at Harvard University, but the lecture hall, which was completed at the same time, had a bad reputation for having excessively long reverberation, making speeches extremely difficult to understand. To address this, the then-president commissioned Sabine, a 27-year-old assistant professor, to investigate. Sabine first measured the time it took for the end of a speaker's words to linger in the room and become inaudible. It was 5.5 seconds, which was enough time for 12 to 15 words to be spoken, and he found that the words were overlapping one after the other, resulting in poor clarity. Based on his experience that the length of reverberation in a room is shortened by soft materials such as cushions, Sabine tried an experiment in which he brought a large number of cushions into the hall and tried to determine the relationship between the amount of cushions (the length of the hall) and the shortened reverberation.
The experimental results, as shown in Figure 1 on the next page, revealed that there is a constant relationship between the length of the cushion and the reciprocal length of the resonance. The sound source used was a pipe from a pipe organ that produces a 512 Hz sound. Air was supplied from a compressor to produce a constant volume, and after stopping the sound, the time until it was no longer audible was measured with a stopwatch.
As you may have noticed, this would mean that the measurements cannot be reliable unless the background noise is constant. Sabine 's team apparently repeated the measurements many times when there was no external noise at night. They conducted this type of experiment in various spaces, such as classrooms, and found that the length of the reverberation is determined by the room volume and the sound absorption capacity (now called the equivalent sound absorption area; the sound absorption capacity is the value obtained by multiplying the total surface area of the room by the average sound absorption coefficient).
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Figure 1 shows the linear relationship between sound absorption and the reciprocal of reverberation time.
Sabine was subsequently entrusted with the acoustic design of Boston Symphony Hall (home to the Boston Symphony Orchestra, one of America's leading orchestras, where Seiji Ozawa served as music director for nearly 30 years until 2002), which is still considered one of the top five acoustic venues, and he achieved the reverberation time values he had predicted. For more than 100 years since then, this reverberation time has remained the most basic and important indicator of the acoustic performance of a room.
Now, the so-called top five concert halls in the world, including the Boston Symphony Hall, were all built in the latter half of the 19th century. Incidentally, the Musikverein in Vienna, famous for its New Year's Concert, is also one of them.
In this field, it's often ironically said that concert halls built before the theory of reverberation was established still have the best acoustics, implying that room acoustics as a science hasn't made a practical contribution. However, these buildings are exceptionally good halls that survived the natural selection process, and since then, many concert halls and opera houses have been built that reflect the results of various room acoustic studies. Many halls around the world now have acoustics that are no less impressive than those of late 19th-century concert halls. Discussing the quality of acoustics would require countless pages of paper and cover a wide range of perspectives, so I'll leave it at that.
In any case, reverberation time is the most important and reliable physical indicator when discussing the acoustics of a hall. However, even with the same reverberation time, some halls may have drastically different evaluations, and even in highly-rated halls, it is difficult to eliminate all seats with poor sound quality. Since reverberation time is based on the premise of a diffuse sound field, only one can be defined in a room, and it is an indicator that cannot measure differences in this regard.
Thus, reverberation time alone is insufficient for designing the acoustics of a hall. Current concert hall acoustic design incorporates various indicators, including the room sound pressure distribution, the energy ratio of early reflections to rear diffused sound (sound clarity and separation), and physical indicators that correlate highly with the "feeling of being enveloped in sound" using signals entering both ears.
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- Reference book: "The Physics of Music" by Alexander Wood, Davies Press, 2008.
- Figure 1 was created based on Fig. 13.1 from the above-mentioned book.
(Excerpt from the email newsletter issued on August 26, 2010)
