A NON-DIRECTIONAL MICROPHONE 417 



Ao = effective area of diaphragm, 



;,?(, = effective mass of diaphragm, 



To = mechanical resistance of diaphragm. 



So = stiffness of diaphragm, 



Yi = volume of air under diaphragm, 



ffio = equivalent mass in coil slot, 



r2 = equivalent mechanical resistance in coil slot, 



A2 = total area of coil slots, 



V, = volume of air chamber in front of resistance ring, 



;»4 = equivalent mass of air in acoustic resistance silk, 



Ti = mechanical resistance to air flow in silk, 



Ai = total area of holes in silk, 



V-o = volume of case, 



rr = equivalent mechanical resistance of tube, 



mr = equivalent mass of air in tube. 



At = area of tube, 

 i'-i, 0, 2, 4 = linear velocities, 

 x^i, 0, 2, 4 = linear displacements, 



Po = atmospheric pressure, 

 X = ratio of specific heats for a gas, 



.^ = mechanical impedance (Force and \'elocity are both 

 ^ ^ ^ complex quantities), 



— . — = stiffness coefificient. 



Displacement 



The Lagrangian equations for a system with four independent co- 

 ordinates can be written in the form : 



f(f)+ll+IZ=eM) («= -1,0,2,4), 



at \ dXn I OXn OXn 



(1) 



in which T is the kinetic energy, F is Rayleigh's dissipation function, 

 V is the potential energy, and e„(/) is a periodic force. The kinetic 

 energy of the system is 



T = |m_ii--r + iwoi'o- + ^^2^-2' + ^w,.rA (2) 



Rayleigh's dissipation function becomes 



F = hr-ix-i' + hr.x^ + lr2X2' + Ird^, (3) 



