198 



MICROPHONES 



where ^9 and ^e+iso may be obtained from equation 9.42. The acoustic 

 impedance of the ribbon, Fig. 9.17, is given by 



Zar = Jo}Mar — 



;C 



9.46 



0}L,AR 



where Mar = inertance of the ribbon, and 



Car = acoustic capacitance of the rib- 

 bon. 



From equation 9.21 the total force of the air 

 load upon the ribbon is 



/ma — 



JWpUr 



—ff^S'ff-^''''^ 9.47 



Fig. 9.17. A ribbon microphone 

 with a large circular baffle. 



The above integration extends over both sides of the ribbon and cog- 

 nizance must be taken of the 180° difference in phase between the front 

 and back when integrating between the two surfaces. The integration of 

 equation 9.47 may be carried out by dividing the ribbon into small ele- 

 ments and carrying out the indicated integration. 



The acoustic impedance of the air load is 



/ma 



ZaA = rAA +JXAA = 



^ff^«r 



joit 



9.48 



The acoustic impedance Zas of the slit between the ribbon and pole pieces 

 is given by equation 9.23. 



The resonance of the ribbon is usually placed below the audible limit. 

 Therefore, the acoustic capacitance of the ribbon may be neglected. The 

 acoustic resistance Taa of the air load is negligible save at the very high 

 frequencies. The fundamental resonance of the ribbon is located below 

 the audible range and the negative reactance term in equation 9.46 may 

 be neglected. Under these conditions the acoustic impedance of the 

 vibrating system is 



zaf = joiMAR + Jo)Maa 9.49 



where Maa = inertance of the air load. 



The velocity, in centimeters per second^ of the ribbon is 



X = 



^RZj 



9.50 



where ^r = area of the ribbon, sauare centimeters. 



