A NONDIRECTIONAL MICROPHONE 421 



ciuestioii, // is the width of the slot, r- is the pressure gradient and ^ is 



ox 



the coefficient of viscosity of air J If m is the mass per unit volume, the 



kinetic energy for a unit length of the slot and for a unit length along 



the circumference is 



'^'(^ r "^''iz. (7) 



1 r"m I d 



2 Jo ^'U 



K.E. =^ 1-1^ 



dx 



The same kinetic energy expressed in terms of the average linear ve- 

 locity and the effective mass of the whole width is 



K.K. = -^ nir 



2 "-..2 



h_ 



12 



dp 

 dx 



(8) 



Comparing the integrated expression of (7) with (8) we find that the 

 ratio of the effective mass to the physical mass in the slot is _ , that is 



m2 = c mass of two slots. 



Knowing the average linear velocity in the slot it is quite simple to 

 calculate the mechanical resistance as 



24 /x ItD 

 '' = ^h 



If the diameter of the coil is large compared to the air passages then D 

 can be taken to be the diameter of the coil. 



The constants Tq and Sq can be found from the location and magnitude 

 of the resonant peak when the diaphragm is not damped by any ex- 

 ternal resistance. In making such measurements it was found that ro 

 was a function of frequency. It is sufficient, however, to choose an 

 average value because ro is usually small as compared to the resistance 

 of the damping ring, mo is again calculated from a consideration of the 

 kinetic energy. If the diaphragm behaves like a simple piston the 

 dome-shaped center portion will have the same velocity at all points. 

 For the annulus we may assume parabolic deflection. The inner 

 region plus the effective mass of the outer annulus make up mo. 



When w^e consider the grid we again make the assumption that the 

 air in the holes moves like a slug, and that the frictional losses due to the 

 walls can be neglected. Even the impedance due to the effective mass 

 of the slug itself is less important than its radiation impedance. Since 

 the latter is a function of frequency it is necessary to change r-i and 

 w_i for each frequency which is being considered. An account of a 



