284 ARCHITECTURAL ACOUSTICS 



where po = pressure, in dynes per square centimeter, obtained at a distance 

 ^0, in centimeters. 



To obtain the pressure for a point not on the axis, the above equation 

 must be multipHed by a factor obtained from the directional characteristic 

 at this frequency. The direct radiation from the loud speaker can then 

 be obtained for any point in the space. 



The energy density, ergs per cubic centimeter, due to direct radiation 

 from the loud speaker is 



£. = i^ ■ 12.5 



where Rg = ratio of the sound pressure at angle 6 to 9 = Q, 



p = density of air, in grams per cubic centimeter, and 

 c = velocity of sound, in centimeters per second. 

 To analyze the distribution of the direct sound over the area, the plan 

 view of the theatre and the directional characteristics of the reproducer in 

 the horizontal plane must be considered. The angle subtended at the loud 

 speaker by the area to be covered will determine the effective dispersion 

 angle of the reproducer. The sound energy density due to the generally 

 reflected sound is a function of the absorption characteristics of the theatre 

 and the power output of the reproducer. The sound energy density, ergs 

 per cubic centimeter, due to the generally reflected sound is given by 



En=^[\ - e^"' "°^' (^-"^^ ')/^n(l - «) 12.6 



cao 



where a = the average absorption per unit area, absorption coefficient, 

 tS = the area of the absorbing materials, in square centimeters, 

 P^ = the volume of the room, in cubic centimeters, 

 / = time, in seconds, 



c = the velocity of sound, in centimeters per second, and 

 P = the power output of the loud speaker, in ergs per second. 

 The total sound energy density at any point in the theatre will be the 

 sum of the direct and the generally reflected sound, and may be expressed by 



Et = Ed + Er 12.7 



On pages 282 and 283 a method was outlined, employing directional loud 

 speakers, for obtaining a uniform energy distribution of the direct sound. 

 The energy density of reflected sound, as shown by equation 12.6, is in- 

 dependent of the observation point. As a consequence, by employing 



