SINGLE COIL, SINGLE CONE LOUD SPEAKER 113 



where mi = mass of the voice coil, in grams, 



p = density of the voice conductor, in grams per cubic centimeter, 



and 

 kr = resistivity of the voice coil conductor, in ohms per cubic cen- 

 timeter. 



From the standpoint of maximum efficiency it is desirable to make the 

 mass of the cone as small as possible. The maximum efficiency occurs 

 when the mass of the coil is equal to the air load mass plus the cone mass. 

 To fulfill this condition is not practical save at the high frequencies. 



The impedance and efficiency characteristics of loud speakers with 

 16-inch, 4-inch, and 1-inch diameter cones are shown in Fig. 7.1. The 

 air load resistance and reactance is assumed to be the same as that on the 

 two sides of a vibrating piston with the diameter equal to the cone diameter. 

 See Sec. 5.7. The weight of the cone and voice coil of the 16-inch cone 

 are typical of loud speakers of this size in use to-day. The efficiency has 

 been computed assuming that all parts of the cone move with the same 

 phase. The constants of the 4-inch and 1-inch cones were chosen to yield 

 approximately the same efficiency as the 16-inch cone. A comparison of 

 the characteristics shows that it is possible to obtain efficiency comparable 

 to that of the large cone over a wide range by using a small cone and coil 

 system. Of course, the power handling capacity of the 1-inch diameter is 

 very small at the low frequencies. 



The power output, in ergs per second, of a vibrating piston is 



ruAX^ 



7.5 



where rMA = mechanical resistance, in mechanical ohms, from Sec. 5.7, and 

 X = rms, velocity of the piston, in centimeters per second. 



Equation 7.5 may be used to compute the power output of a direct radi- 

 ator loud speaker as a function of the frequency. 



The peak amplitude frequency characteristics of a 16-inch, 4-inch and 

 1-inch piston mounted in an infinite baffle for one watt of sound output 

 are shown in Fig. 7.2. These characteristics show that a relatively large 

 piston is required to deliver adequate power at the lower frequencies. In 

 addition, a relatively heavy cone is required in order to prevent generation 

 of harmonics due to spurious vibrations of the large surfaces. 



The characteristics of Fig. 7.1 show that a mass controlled system delivers 

 constant output below the point of ultimate resistance. To deliver con- 

 stant output in the range where the resistance is constant the mechanical 

 impedance of the entire system must be independent of the frequency. 



