## 05 Jul Small rooms and reverberation time

To quote Professor Doug Jones: “The acoustics of small rooms is dominated by modes, shape, and reflection management. Acousticians who build large rooms are frequently frustrated with small room design because few of the intellectual tools of the trade that work in large rooms can be applied to small rooms. Getting small rooms to sound right involves art and science. The science part is mostly straight forward. The creative part is quite subjective and a great sounding small room can be just as elusive as a great sounding concert hall.”

So what is a small room? Manfred Schroder defines them as follows; A large room for speech with a low frequency limit of 80 Hz is = to or >991 m³ (35,000 ft³) and a large room for wide range music with a low frequency limit of 30 Hz is = to or >7079 m³ (250,000 ft³). Right, obviously acoustically large or small is a frequency dependant phenomenon but surely by definition most of us are working / listening in non statistical small acoustical spaces.

The question really becomes centered on the definition of reverberation. Wallace Clement Sabine who first formulated the equation to calculate reverberation time described reverberation in this way: “Reverberation results in a mass of sound filling the whole room and incapable of of analysis into its distinct reflections” Meaning, for true reverberation to exist, there needs to be a homogeneous and isotropic sound field. Usually such conditions are approached in physically large rooms that do not contain much absorption.

Unfortunately reverberation is popularly understood to be equivalent to decay. Sabine also wrote: “The word ‘resonance’ has been used loosely as synonymous with reverberation and even with echo and is so given in some of the more voluminous but less exact popular dictionaries. In scientific literature the term has received a very definite and precise application to the phenomenon where ever it may occur. A word having this significance is necessary; and it is very desirable that the term should not, even popularly, by meaning many things, cease to mean anything exactly.”

This is where we are today. Without rigorous definition and application of the concept of reverberation we are left with something that ceases to mean anything exactly. Who really cares right? Isn’t it just semantics? Prof Doug Jones: “It is generally accepted that in small rooms after approximately four to six bounces, a sound wave will have lost most of its energy to the reflecting surfaces and will become so diffuse as to be indistinguishable from the noise floor. This of course depends on the amount of absorption in the room.”

In a 4.9m x 3.3m x 2.4 m (12’ X 16’ X 8’) room a single wave will take less than 33 ms to bounce five times and be gone. Don Davis: “It should always be considered that, insofar as the reverberation formulas depend on the statistical averages, they presuppose a complete mixing of sound in the room. In very absorptive rooms the sound dies away in a few reflections, and the statistical basis of the formulas is weakened.”

“Spaces that qualify as “large rooms” can effectively utilize the myriad of equations based on the original assumptions of Sabine for his reverberation equations. In spaces exceeding these volumes and with an RT60 of 1.6 seconds or greater, we will find mixing homogenous sound fields of sufficient density to allow accurate engineering estimates of the level of each.”

Don Davis: “What is often overlooked in the attempted measurement of RT60 in small rooms is that the definition of RT60 has two parts, the first of which is unfortunately commonly overlooked.

1 RT60 is the measurement of the decay time of a well mixed reverberant sound field well beyond Dc, a real critical distance.

2 RT60 is the time in seconds for the reverberant sound field to decay 60 dB after the sound source is silenced.

Since in small rooms, there is no Dc, no well mixed sound field, hence, no reverberation but merely a series of early reflected energy, the measurement of RT60 becomes meaningless in such environments.

What becomes meaningful is the control of early reflections because there is no reverberation to mask them.”

Fundamental point: modal decay rates are not reverberation. Reverberation is “the time in seconds that it takes a diffuse sound field, well beyond a real critical distance, to lower in level by 60 dB when the sound source is silenced.” Modal decay rates are dB-per-second (dB/s) rate of decay for a specific modal frequency.

In the end, one place to start is to avoid the use of an equation that is nonsensical in its application.

Once more, Don Davis: “One hundred eight reflections allow a reasonable statistical sample. When small absorptive spaces such as control rooms in recording studios, small classrooms, etc., are computed the inapplicability of statistical equations becomes apparent because of the low N. Such enclosures do indeed have a finite number of reflections that are best handled by careful Envelope Time Curve (ETC) analysis and specific rather than statistical treatment of the indicated surfaces.”

Don Davis quotes from Sound System Engineering 4th Edition

Doug Jones quoted from Handbook for Sound Engineers 4th Edition

W.C. Sabine. Quoted from Collected Papers on Acoustics, Cambridge, MA: Harvard University Press, 1922