STEADY STATE LOUD SPEAKER MEASUREMENTS 137 



of different kinds, etc. can of course be used but these in general are 

 considerably more difficult to use than the condenser transmitter, 

 especially for free space acoustic measurements and the measured 

 quantities bear no more simple relation to the acoustic power or energy. 

 Assuming the condenser transmitter then to be the acoustic measur- 

 ing or indicating device, the problem becomes one of how and where in 

 the medium to measure the pressure so that the measurement will bear 

 some readily deducible relation to the acoustic power delivered by the 

 loud speaker. The answer depends upon the nature of the acoustic 

 medium in which the measurements are made. The simplest relations 

 between excess r.m.s. pressure in the medium and the acoustic power 

 exist when the pressure measurements are made in an infinite medium 

 or in a room in which the incident energy at the walls is completely 

 absorbed. Under such conditions the acoustic power from a loud 

 speaker could be obtained by measuring the pressure at all points on 

 the surface of a sphere having a radius several times that of the largest 

 dimension of the sound radiating surface and with the sound radiating 

 surface at the center of the sphere. The acoustic power would then be 



Pa - 



yjff^ds,^ (3) 



where p is the density of the air; c is the velocity of sound propagation ; 

 p is the excess r.m.s. pressure; and ds is the surface of the sphere. 

 This relation, however, is generally true only when the radius of the 

 spherical surface is sufficiently large so that the sound radiating 

 surface appears as a point source. From equations (1), (2) and (3) the 

 efficiency of a loud speaker could then be expressed in terms of excess 

 pressure measurements over the surface of the sphere in an infinite 

 medium as follows : 



If 



p-ds 



^Pa^ 



"^ Pe PC e^ 

 4r 



(4) 



K \ \ pHs 



e~ 

 r 



Within an enclosure where there are sound reflections from the 

 bounding surfaces, the determination of the acoustic power deli\ered 

 by a loud speaker would involve the measurement of the pressure at 



2 "Theory of Vibrating Systems and Sound," Crandall, pp. 92 and 120. 

 10 



