138 DIRECT RADIATOR LOUD SPEAKERS 



7.16. Transient Response. — The subject of transient response em- 

 braces a wide variety of physical phenomena. Electric transients concern 

 electrical circuits and the components of electrical systems. Acoustic 

 transients concern acoustical and mechanical systems. In view of the 

 fact that the sound reproducing and collecting systems are mechanical, the 

 general tendency is to assume that these systems exhibit very poor transient 

 response characteristics. In properly designed acoustical elements the 

 performance is very often far superior to the other components used in 

 sound reproducing systems. 



The behavior of a loud speaker may be analyzed by solving the differen- 

 tial equations of the dynamical system. In other words, find the velocities 

 of the elements of the system which, when substituted in the differential 

 equations, will satisfy the initial and final conditions. The solution of a 

 differential equation may be divided into the steady state term and the 

 transient term. The operational calculus is of great value in obtaining 

 the transient response of a mechanical or acoustical system to a suddenly 

 impressed force or pressure. 



The general analysis used by Heaviside is applicable to any type of vi- 

 brating system whether electrical, mechanical or acoustical. It is the 

 purpose of this section to show the response of the conventional direct 

 radiator loud speaker to a suddenly applied unit force. 



The equivalent circuit of the dynamic loud speaker at the low frequencies 

 is shown in Fig. 7.3. The differential equation for the system of Fig. 7.3 is 



X 



mx -\- tmtx + — =Jmo 7.12 



where x = displacement, 



/mo = mechanical driving force, in dynes, 



m = mass, in grams. 

 Cm = compliance of the suspensions system. In centimeters per 



dyne, and 

 ^MT = total mechanical resistance, mechanical ohms. 

 The total mechanical resistance is 



fMT = TmS + Tmr + rME 7.13 



where Vms = mechanical resistance due to losses in the suspension system, 

 etc., in mechanical ohms, 

 rMR = mechanical radiation resistance, in mechanical ohms, and 

 Tmb — mechanical resistance due to the electrical system, in me- 

 chanical ohms. 



