ACOUSTIC IMPEDANCE. O 



z 



pedance dois-if;/, will l)e ] = - vector acoustic ahsolnns per sq. cm. 



o 



F 

 Or, if Ave employ ii \'ibiomotive pressure intensity j) — ^^ vector maxi- 

 mum cyclic tlynes per sq. cm. to actuate the disk; then p being taken 

 with standard phase: 



_ p acoustic absohms , . 



X sq. cm. 



or ;r = — = rms. cm. per sec. Z (4) 



I Ix + h 



The dimensions of acoustic impedance, as derived from (2), are ]MT~'j 

 or mass per unit of time (force divided by velocity). The dimensions 

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

 MT-i/Ll 



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

 diaphragm is therefore the opposition to the development of vibra- 

 tional velocity at that surface under impressed vmf. Although when 

 so defined, acoustic impedance invoh-es 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 tul)e, but may occur in a region of any shape. 



We liaA'e hitherto assumefl that the \-elocity .r was the same at all 

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

 diaphragm, however, such as a telephone-receiver diaphragm, the 

 vibrational displacement x, and velocity x, will be different at different 

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

 c?S of the surface of the disk, at which the velocity is x rms. kines, the 

 power of this motion is 



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



where x is taken as of standard phase and zero slope. Of this power, 

 the real component is dissipated, and the iinaginar\- component is 

 cyclically stored and released. The total power deli\'ered to the disk, 

 including both sides, will be 



P = / '.r- s f/S = S / '■*•' dH abwatts Z (6) 



