RECEIVERS AND MICROPHONES 



567 



is the effective mass, Sq the stiffness, ro, the mechanical resistance of 

 the diaphragm, and /^e'"' the alternating force acting upon the dia- 

 phragm. The absolute value of the velocity of the diaphragm is 

 gi\'en by 



F 



V = 



m 



4A2 + 



COo" 



1/2 



and the amplitude by i^/co where A = ~ — , the damping constant, 



and 



Wo 



_ ^0 



iiL = 211 X resonant frequency. The velocities and ampli- 



niQ 



tudes for a constant force and for two different values of A, calculated 

 from these expressions, are graphically represented in Fig. 1. Both 

 the amplitude and velocity curves show wide variations in response 

 with frequency. They indicate that for small variations in amplitude 

 the resonant frequency must be near the upper limit of the frequencies 

 to be transmitted and for small variations in velocity the damping 

 constant must be high. But instruments designed on this basis would 

 be relatively insensitive even if such conditions could be met readily 

 in their construction. 



In the design of electrical networks for the transmission of wide 

 frequency bands the end is attained by the combination of more than 

 one resonant circuit. We can advantageously resort to a similar 

 expedient in a mechanical system by the use of a structure more 

 complicated than one having a single degree of freedom. The dia- 

 phragm may be coupled to another mechanical or acoustical network 

 of the proper type so as to give us the desired uniformity of response. 

 The circuit diagram of one such mechanical network is shown in Fig. 2, 



jnrioCJ 



_So 



To 



FeJ^^0-r^ 



jm|U) 





Fig. 2 — ^Circuit diagram for receiver or microphone. 



where S\ is the stiffness, nii the mass, and fi the resistance of the 

 elements of the coupled network. The construction of a mechanical 

 system represented by this diagram is brought out in detail in the 



