The calibration of E.A.R

E.A.R is primarily intended to give an artistic impression of the spatial acoustics and auditory experience of a configuration of sound sources, listeners and geometry. Therefore striving for scientific accurateness was not one of the main goals. Nevertheless it is important to have an understanding of how E.A.R performs in relation to the existing body of literature.

Reverberation time

One of the most studied subjects in the field of architectural acoustics is the reverberation time of a room. It has a tremendous impact on the quality and appearance of a music hall and hence has been the subject of thorough examination. Several formulas have been conceived based on empirical study that seem to predict the reverberation time of a room pretty well within some well known constraints.

The formulas by Sabine (1) and Norris-Eyring (2) predict the RT60 reverberation time, or the time for the reflections of a direct sound to decay by 60 decibels below the level of the direct sound itself. This is also a property that is easily derived from an impulse response as rendered by E.A.R. Hence it allows for a comparison between the outcome of E.A.R. and the values that the formulas predict.

The formulas predict the reverberation time, operating on the volume and surface area of the enclosing shape. The weighted average absorption of the surface . The attenuation coefficient for air absorption , the latter not always accounted for in the literature.

The graphs and tables below show that the reverberation times calculated by E.A.R do not deviate that much from Norris-Eyring. The deviation is largest in very reverberant rooms, higher values in large rooms while giving lower values in small rooms. The fourth graph shows the effect that the specularity has on the reverberation time. Higher values for specularity yield a higher average path length in-between of reflections, hence higher specularity results in a longer reverberation time. Since specularity of the material is not incorporated in both the Sabine formula as the Norris-Eyring formula, choosing the speculairy value for the material in E.A.R is somewhat arbitrary. The deduction of the Norris-Eyring formula seems to imply a perfectly specular material, but for these series of tests a specularity of 0.5 has been used unless stated otherwise. The fifth graph shows how increasing air attenuation decreases the reverberation time.

 0,050,150,250,350,450,550,650,750,850,95
E.A.R.1,8080,5850,3320,2300,1680,1230,0970,0780,0510,040
Sabine2,0570,6860,4110,2940,2290,1870,1580,1370,1210,108
Norris2,0050,6330,3570,2390,1720,1290,0980,0740,0540,034
 0,050,150,250,350,450,550,650,750,850,95
E.A.R.3,0621,0050,5690,3820,2980,2080,1610,1230,0930,068
Sabine3,1181,0390,6240,4450,3460,2830,2400,2080,1830,164
Norris3,0390,9590,5420,3620,2610,1950,1490,1120,0820,052
 0,050,150,250,350,450,550,650,750,850,95
E.A.R.10,3843,3641,8361,2980,9020,6720,5510,4250,2860,203
Sabine9,6663,2221,9331,3811,0740,8790,7440,6440,5690,509
Norris9,4222,9741,6801,1220,8080,6050,4600,3490,2550,161
 0,050,150,250,350,450,550,650,750,850,95
spec:0.02,2410,7470,4370,3050,2260,1720,1310,1030,0800,059
spec:0.53,0621,0050,5690,3820,2980,2080,1610,1230,0930,068
spec:1.05,9161,9080,9620,6740,5090,3480,2410,1820,1250,078
 00,010,020,030,040,050,060,070,080,090,10,110,120,130,140,150,160,170,180,190,2
E.A.R.9,9553,0321,8341,2840,9510,7840,6430,5150,4970,4420,3680,3300,3120,2630,3010,2620,2330,2130,1830,1810,179
Sabine9,6662,8431,6671,1790,9120,7440,6280,5430,4790,4280,3870,3530,3240,3000,2790,2610,2450,2310,2190,2070,197
Norris9,4222,8211,6591,1750,9100,7420,6270,5420,4780,4270,3860,3520,3240,3000,2790,2610,2450,2310,2190,2070,197