242 BELL SYSTEM TECHNICAL JOURNAL 



Besides the requirement on frequency response just discussed, the 

 system also must be capable of handling sound powers that vary 

 through a very wide range. If this discussion were limited to the type 

 of symphonic music that now is produced by the large orchestras, this 

 range would be about 10,000,000 to 1, or 70 decibels. To reproduce 

 such music then, the system should be capable of handling the smallest 

 amount of power without introducing extraneous noises approaching 

 it in intensity, and also reproduce the most intense sounds without 

 overloading any part of the transmission system. However, this range 

 is determined by the capacities of the musical instruments now avail- 

 able and the man power that conveniently can be grouped together 

 under one conductor. As soon as a system was built that was capable 

 of handling a much wider range, the musicians immediately took 

 advantage of it to produce certain effects that they previously had 

 tried to obtain with the orchestra alone, but without success because 

 of the limited power of the instruments themselves. For these 

 reasons it seems clear that the desirable requirements for intensity 

 range, as well as those for frequency range, are determined largely by 

 the ear rather than by the physical characteristic of any sound. An 

 ideal transmission should, without introducing an extraneous audible 

 sound, be capable of reproducing a sound as faintly as the ear can hear 

 and as loudly as the ear can tolerate. Such a range has been deter- 

 mined with the average normal ear when using pure tones. The 

 results of recent tests are shown in Fig. 1. 



The ordinates are given in decibels above the reference intensity 

 which is 10~'^ watts per square centimeter. The values are for field 

 intensities existing in an air space free from reflecting walls. The 

 most intense peaks in music come in the range between 200 and 1000 

 c.p.s. Taking an average for this range it may be seen that there is 

 approximately a 100-db range in intensity for the music, provided 

 about 10 db is allowed for the masking of sound in the concert hall 

 even when the audience is quietest. 



The music from the largest orchestra utilizes only 70 db of this 

 range when it plays in a concert hall of usual size. To utilize the full 

 capabilities of the hearing range the ideal transmission system should 

 add about 10 db on the pp side and 20 db on the^ side of the range. 

 The capacity of the sound projectors necessary to reach the maximum 

 allowable sound that the ear can tolerate varies with the size of the 

 room. A good estimate can be obtained by the following consider- 

 ation. 



If T is the time of reverberation of the hall in seconds, E the power 

 of the sound source in watts, / the maximum energy density per cubic 



