80 ACOUSTICAL ELEMENTS 



where dV is the change in the original volume V. 



dv = Sx = X 5.6 



where x = displacement, in centimeters, over the area 6", in square cen- 

 timeters, and 

 X = volume displacement, in cubic centimeters. 

 From equations 5.4, 5.5 and 5.6 



p pc^ 



The ratio X/p is termed the acoustic capacitance by definition. See 

 Sec. 4.4C Therefore the acoustic capacitance of a volume is 



V 

 Ca = — 5.8 



pr 



The next consideration will be an acoustic capacitance combined with 

 an acoustic resistance. The acoustic impedance of a cavity in which 

 the boundaries or a portion of the boundary is terminated in an acoustic 

 resistance is 



^A .„ 



za = z——. — 5.9 



where ta = acoustic resistance of the boundary, 



Ca = acoustic capacitance of the volume, in cubic centimeters per 

 second, 

 CO = Itt/, and 

 / = frequency, in cycles per second. 



5.7. Resistive and Reactive Load upon a Vibrating Piston ^' s- ^. — 



The mechanical impedance of the air load upon one side of a vibrating pis- 

 ton set in an infinite baffie is 



Zm 



,;jv(l-^)+.^^.(««) 5.10 



where R = radius of piston, in centimeters, 



p = density, in grams per cubic centimeter, 



c = velocity of sound, in centimeters per second. 



^ Rayleigh, " Theory of Sound," Macmillan and Co., London. 



^ Crandall, " Vibrating Systems and Sound," D. Van Nostrand Co., New York. 



^ Stewart and Lindsay, " Acoustics," D. Van Nostrand Co., New York. 



