RECORDING AND REPRODUCING OF MUSIC AND SPEECH 519 



from Equation (15), and the impedance looking at a horn whose small 

 end area equals ^2 is 



z,, = ro = A2G (17) 



Substituting 



^2= 13 sq. cm. 



G =41 ohms per cm.^ 

 we get 



2/( =^0 = 533 mechanical ohms 



This is entirely insufficient so that the air-chamber transformer be- 

 comes necessary. 



To calculate the necessary ratio of areas on the two sides of the air- 

 chamber transformer, the following formula is needed. The formula 

 assumes the chamber to be relatively small compared with all wave 

 lengths of the sound to be transmitted, that is, the pressure changes 

 throughout the chamber are substantially in phase. 



where 



Zo = the impedance of the primary side of the transformer in me- 

 chanical ohms; 



Zh = the impedance on the secondary side of the transformer in 

 mechanical ohms, i.e., the horn impedance; 



j;i = mechanical current, i.e., velocity on the primary side of the 

 transformer in centimeters per second; 



i'2 = mechanical current on the secondary side of the transformer 

 in centimeters per second; 



Fi = alternating force on primary side of air-chamber transformer 

 in dynes; 



/''2= alternating force on secondary side of air-chamber transformer 



in dynes; 

 /I Ineffective area working into the primary side of the air-chamber 

 in centimeters squared; 



yl2=effective area working into the secondary side of the air- 

 chamber in centimeters squared. 



The characteristic impedance of the line on the diaphragm or 

 primary side of the air-chamber as shown by equation (15) is 



Trfcm 



(19) 



From Equation (17) the characteristic impedance on the horn or 

 secondary side is 



Zh = GA2. (20) 



