288 ARCHITECTURAL ACOUSTICS 



Rg = ratio of the pressure at the angle d to d = 0^ 

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

 c = velocity of sound, in centimeters per second. 



The problem is to select a loud speaker with suitable directional char- 

 acteristics, see Sec. 12.2B, and then to adjust the power output and orien- 

 tation so that the sum Em + Ed2 of equations 12.8 and 12.9 is a constant 

 for all parts of the listening area of the theatre. The intensity level on the 

 orchestra floor, in Fig. 12.4, due to the direct sound from a loud speaker 

 having directional characteristics as shown, is given by the curve L. The 

 intensity level due to the combination of the original sound and augmented 

 sound from the loud speaker is shown by curve T of Fig. 12.4. The re- 

 sultant intensity is quite uniform over the orchestra floor. A similar analy- 

 sis will show that the intensity level in the balcony is also relatively uni- 

 form. Further consideration of the characteristic of Fig. 12.4 shows that 

 the total intensity level characteristic remains uniform when the output 

 of the loud speakers, that is, the gain in augmented sound, is varied over 

 wide limits. 



The energy density, in ergs per cubic centimeter, in the theatre due to 

 generally reflected sound is 



^^ ^ HPd,+Pd2) ^^ _ ^(,s [log, (1-a)] 0/4F](l _ ^) 12.10 



caS 



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

 S = area of absorbing materials, in square centimeters, 

 F = volume of the theatre, in cubic centimeters, 

 / = time, in seconds, 



c — velocity of sound, in centimeters per second, 

 Pdi = power output of the original sound, in ergs per second, and 

 Pd2 = power output of the loud speaker, in ergs per second. 

 The aid obtained from reflected sound in a directional sound re-enforcing 

 system is relatively small, ranging from 2 to 6 db. 



The microphones for collecting the sounds are usually concealed in the 

 footlight trough. 1^ By employing directional loud speakers, as outlined 

 above, the sound level at the microphones due to the loud speakers is low 

 and thereby reduces the tendency of acoustic feedback or regeneration in 

 the reproducing system. In large theatres, having an expansive stage, the 

 pickup distance will be very large. Consequently, the sound which reaches 

 the microphones from the original source will be small and will require con- 



12 Olson, H. F., RCJ Review, Vol. 1, No. 1, p. 49, 1936. 



