138 BELL SYSTEM TECHNICAL JOURNAL 



all points within the enclosure in order to obtain the average energy 

 density and then making use of known relations between energy 

 density and the rate of energy flow into the room. Under steady 

 state conditions, the total potential energy stored within the room 

 would be 



Assuming the room to be large so that the region within say a wave- 

 length of the loud speaker is a small portion of the total volume of the 

 room, it can be said with a reasonable approximation that the potential 

 and kinetic energies stored within the room as the sound is transmitted 

 are equal. The total energy would therefore be twice the potential 

 energy or 



This latter statement may be roughly justified in a simple manner by 

 considering the sound radiated by the loud speaker as consisting of two 

 components, one of which is completely absorbed at the walls and the 

 other completely reflected. In considering separately that component 

 which is absorbed, the loud speaker can be thought of as in an infinite 

 medium and under these conditions (excluding the region within say a 

 wave-length of the loud speaker) the acoustic impedance of the medium 

 is essentially non-reactive. The potential and kinetic energies of the 

 sound transmitted would therefore be equal. That component which 

 is transmitted to the medium and completely reflected at the walls 

 produces an ideal standing wave system. In such a system along the 

 direction of the standing wave the total energy is alternately all 

 kinetic and all potential and since this transition takes place the 

 potential and kinetic energies must be equal. 



Considering the room volume V, the average energy density would be 



^ = ^11 h'"^- ('> 



If the loud speaker emits power into the room at a rate Pa, the 

 average energy density in the room after a steady state has been 

 reached is 



E = ^, (8) 



' "The Dynamical Theory of Sound," Lamb, p. 208, Second Edition. 

 * "Theory of Vibrating Systems and Sound," Crandall, p. 210. 



