Characterizing rooms …1 Characterizing rooms regarding reverberation time prediction and the sensitivity to absorption and scattering coefficient accuracy Bengt-Inge Dalenback, CATT Mariagatan 16A, SE Gothenburg, SWEDEN Sarah G. Brown, RPG Diffusor Systems, Inc. 651-C Commerce Dr., Upper Marlboro, MD 20774, USA

Characterizing rooms …2 Introduction Prediction of reverberation time RT (more specifically T 30 ) using ray-tracing and similar algorithms naturally requires realistic input data, but the degree of data accuracy required varies with the room properties In some types of rooms accurate coefficients are crucial while in other types it is less crucial and the prediction results are less sensitive to the input data. This presentation will focus on the scattering coefficients, since they are the hardest to estimate and often have a big impact on the RT prediction, but first some rather obvious notes about the absorption coefficients:

Characterizing rooms …3 Introduction cont. 1.An accurate absorption coefficient for a certain material is only crucial if the relative surface area of that material is big, especially if it is the dominating material 2.If a small patch of concrete is used in a hall, it does not matter if a coefficient of 0.01 or 0.02 (or even 0.05) is used, but if the room is all concrete (e.g. a reverberation chamber), the values chosen are critical since going from 0.01 to 0.02 causes a factor of two difference in RT (at frequencies where the air absorption does not dominate) 3.If a room has many materials of similar areas - errors in absorption coefficient estimates tend to even out However, even if the absorption has been well estimated in some types of rooms, the accuracy of estimation of scattering coefficients can have a very big impact on the RT prediction, and even worse if diffuse reflections are not handled at all While the measurement of absorption coefficient has a range of well known issues, as discussed in this session, there are many more issues with measuring and estimating scattering coefficients.

Characterizing rooms …4 Introduction cont. This paper will attempt to classify rooms, regarding T 30 prediction, according to their sensitivity to the scattering coefficients, due to their shape, geometrical mixing (or diffusing) and absorption distribution Predictions of early/late measures like D 50 are not as sensitive in rooms where the logarithmic decay is curved since they do not rely on fitting a straight line to a non- straight logarithmic decay like T 30 does. At the one extreme are non-mixing geometries with uneven absorption making a good estimate of the scattering coefficients crucial. At the other extreme are mixing geometries and/or with high scattering and a mildly varying absorption distribution where prediction is safer and where estimated, or readily available, absorption coefficients can be used. The estimate of scattering coefficients have limited impact Due to the natural frequency dependence of both absorption and scattering coefficients the classification may also differ between octave-bands predictions in the same room.

Characterizing rooms …5 An Index that predicts how diffuse a soundfield is The Index is calculated by examining aspects of a 3D model that has been built and it is useful for the understanding of RT prediction The Index calculation assumes a room with an open space in the center, like in most normal auditoria, it will not predict well with shapes that are too convoluted or coupled The Index is based on a combination of three sub-indices in the range [0..1]: n : a “non-rectangularity” sub-index d : an absorption distribution sub-index m : a geometry mixing/scattering sub-index

Characterizing rooms …6 n compares the number of cells occupied by surface extents to the number of outer shell cells (a perfectly rectangular room will have n = 0): n : a “non-rectangularity” sub-index

Characterizing rooms …7 d : an absorption distribution sub-index d is based on the average absorption as encountered by rays in x-, y-, and z- directions,  x,  y and  z

Characterizing rooms …8 d cont. Since a high mean absorption in the direction of a small dimension makes a soundfield less diffuse (more two-dimensional) the average absorption in each direction is weighted by the dimensions according to: d = (1 - D x / D sum )  x + (1 - D y / D sum )  y + (1 - D z / D sum )  z )/(3  sum ) where D sum = D x + D y + D z and  sum =  x +  y +  z If the average absorption is the same in x-, y- and z-directions the distribution is even and d = 1

Characterizing rooms …9 m is based on surface angle statistics and scattering coefficients: where a scattering coefficient is considered to have the same essential effect as if a surface is angled away from the principle axis and the effect of each surface is weighted with its relative area. m : a geometry mixing/ scattering sub-index

Characterizing rooms …10 The final Index The final Index [0..1] is calculated as Index = ( n + d + m ) / 3 Each sub-index as well as relative weights may be refined but since the main purpose is educational and to illustrate qualitatively what affects the RT there is no point in carrying it much further and no specific name will be given to the Index. The higher the Index is the more diffuse the sound field will be and the more likely it is that the predicted T 30 will be the same as T Eyring With the current implementation and weighting for an Index > 0.20 T 30 becomes close to T Eyring while for Index < 0.20 T 30 will be longer or even much longer than T Eyring The goal of this paper is to describe how various room features affect the reverberation time in principle, it is highly unlikely that an index such as this could be refined so that it can solve all cases and if a 3D model is anyway required a normal prediction can as well be made giving much more information than an ever so advanced index of this type.

Characterizing rooms …11 Description of the cases To illustrate how the Index works examples will be shown for all combinations of: 3 room shapes: Cubic | Long | Flat 2 absorption distributions : Even | Uneven 2 geometry mixing states : Mixing | Non-mixing 8 scattering coefficients : 0 | 0.05 | 0.1 | 0.2 | 0.4 | 0.6 | 0.8 | 1.0 A total of 3 x 2 x 2 x 8 = 96 combinations

Characterizing rooms …12 3 room shapes (all with a volume of 1000 m 3 )

Characterizing rooms …13 2 absorption distributions (example with Long shape)

Characterizing rooms …14 2 geometry mixing states (example with Long shape)

Characterizing rooms …15 8 scattering coefficients 0 | 0.05 | 0.1 | 0.2 | 0.4 | 0.6 | 0.8 | 1.0

Characterizing rooms …16 An initial example case From this initial example it can be seen that for this case to have a soundfield diffuse enough to give T 30 = T Eyring the scattering coefficients have to be > 0.2 and it is indicated by that the Index is then also  The graph can also be interpreted so that if the “actual” average scattering coefficients are 0.1 but have been estimated to be 0.2 the actual T 30 is likely to be predicted a bit too short. Or, if the average scattering coefficients have been estimated to be 0.05, or worse diffuse reflection is not include at all, the actual T 30 is likely to be predicted too long.

Characterizing rooms …17 Cubic shape

Characterizing rooms …18 Long shape

Characterizing rooms …19 Flat shape

Characterizing rooms …20 Conclusions For successful RT prediction it is necessary to understand the overall properties of a room, including it’s geometry, absorption distribution and surface undulation, so that a sufficient estimate of absorption and scattering coefficients can be made. In some cases it is crucial in other cases not. As an aid it is useful to compare models with scattering off vs 100% scattering to see how the room behaves under these two extremes, if the predicted T 30 differs little the predictions are safer, if they differ considerably a good estimate of scattering coefficients is essential for successful T 30 prediction In cases where a good estimate of scattering coefficients are crucial but difficult the only way may be to calculate with high and low values of the scattering coefficients and bind the T 30 values between limits -.-