ACOUSTIC IMPEDANCE, D 



2 



jM'dancc drtisifi/, will be J = - vector acoustic absohms per sq. cm. 



. . F 



Or, if we employ a vibromotive pressure intensity p = -_^ vector maxi- 



o 



mum cyclic dynes per sc[. cm. to actuate the disk; then ;; beinj; taken 

 with standard phase: 



or 



5 51 + h 



The dimensions of acoustic impedance, as derived from (2), areMT"^? 

 or mass per unit of time (force divided by ^-elocity). The dimensions 

 of acoustic impedance densitv, as derived from (3) are ML"'-T'^ or 

 MT~\/L2. 



The acoustic impedance of a fluid at the surface of a Aibrating 

 diaphragm is therefore the opposition to the development of ^'ibra- 

 tional -velocity at that surface under impressed vmf. Although when 

 so defined, acoustic impedance involves the existence of a diaphragm 

 or mechanical surface, at which the impedance is produced; yet 

 acoustic impedance may be conceived of as occurring at an imaginary 

 surface, such as the cross section of an acoustic tube, and without the 

 interposition of a diaphragm. ^Moreover, acoustic impedance is not 

 confined to a tube, t)ut may occin- in a region of any shape. 



We \vd\e hitherto assumed that the \-elocity .r was the same at all 

 parts of the vibrating disk or diaphragm. In any actual flexible 

 diaphragm, howe^•er, such as a telephone-recei-\er diaphragm, the 

 vibrational displacement .c, and velocity .r, will be different at different 

 distances from the center of the disk. If we take any elementary area 

 f/S of the surface of the disk, at which the velocity is .f rms. kines, the 

 power of this motion is 



f/P = .r- I f/S abwatts or ergs per sec. Z (5) 



where .v is taken as of standard phase and zero slope. Of tliis power, 

 the real component is dissipated, and the imaginary component is 

 cyclically stored and released. The total power flelivered to the disk, 

 including l)0th sides, will be 



P = / '.r- s f/S = S / '.r- f/S abwatts Z (6) 



