RESISTIVE AND REACTIVE AIR LOAD 83 



The impedance per unit area is 



( (kRy+jkR \ 



The resistive and reactive components upon the air load per unit area of 

 a pulsating sphere is shown in Fig. 5.1. It will be noticed that the load 

 upon a pulsating sphere is practically the same as that of a vibrating piston, 



5.9. Resistive and Reactive Air Load upon an Oscillating Sphere. — An 



oscillating sphere is a sphere whose radius remains constant while the 

 sphere executes a movement of translation as a function of the time. The 

 mechanical impedance of the air load upon an oscillating sphere is 



Zm = ;:; — 



\ 4 + k^R' ) 



where R = radius of the sphere, in centimeters, 



p = density, in grams per cubic centimeter, 



k = — -J 

 X 



X = wavelength, in centimeters, and 



c = velocity of sound, in centimeters per second. 



The acoustic impedance of the air load upon an oscillating sphere is 



pc 



Za 



f k^R^+j(2kR + k'R^) \ 



[ TT¥r^ ) ^-^^^ 



127ri?2 



The impedance per unit area of an oscillating sphere is 



/ k'R^ +j(2kR + PR') \ 

 \ 4 + k^R* ) 



pc/ k'R'+j(2kR+k'R') \ _^^ 



zi = ^l . . ,.^, ) 5.16C 



The average reactive and resistive components of the air load upon an 

 oscillating sphere is shown in Fig. 5.1. The load on an oscillating sphere 

 is not uniform. In order to compare the radiation characteristics with 

 those of a piston and a pulsating sphere, the ultimate resistance has been 

 made the same. However, the average impedance per unit area of a vibrat- 

 ing sphere is one third that of characteristics 3 shown in Fig. 5.1. 



The oscillating sphere is an acoustic doublet. See Sec. 2.3. There- 

 fore, the resistance component is proportional to the fourth power of the 

 frequency when the dimensions are small compared to the wavelength. 

 The oscillating sphere represents the direct radiator loud speaker without 

 a baffle. 



