rilYSICAL CHARACTERISTICS OF AUDITION 67 



walls may yield appreciably, particularly in some frequency ranges. 

 The mutual impedance between the receiver and ear drum, is, there- 

 fore, not necessarily a simple stiffness reactance. Also the loads due 

 to it on the thermal receiver and ear drum, which in this case takes the 

 place of the transmitter diaphragm, are not simple stiffness reactances. 

 The constants in the case of the ear system will be denoted by the 

 same letters as those used in the calibration but with the primes 

 dropped, with the exception that the intrinsic impedance of the ear 

 drum is denoted by D. D includes the reactions of the ossicles of 

 the middle ear and the cochlea and is probably a complicated function 

 of frequency. If, as may be expected, nature's design is efficient, 

 then D must be of the same general order of magnitude as the load on 

 the ear drum, M12, of the ear canal. This probably constitutes the 

 largest difference between the calibration and the observational 

 systems. Strictly, of course, the condition for maximum power 

 absorption by the ear drum from the air is that D be the conjugate 

 of the impedance of the load on it due to the unobstructed ear canal. 

 This condition is not obtained in nature because of such requirements 

 placed on the design as protection from injury, etc. 



In the case of the ear, Mi may again be neglected, compared to 

 Zi, and the reactance, M12 ^2 may be neglected. Then 



F = Zi xi, 



O = - M12 xi + (Z) + M2) iz, (2) 



where .V2 represents the velocity of motion of the ear drum. Suitable 

 variations with frequency are implied in each of the " constants " 

 of this system. 



We are now in a position to see just what has been measured and 

 called, for the sake of brevity or want of a better name, " minimum 

 audible pressure " in the first part of this paper. 



Let X\ now represent the velocity of the receiver diaphragm in 

 both systems corresponding to that necessary to obtain a minimum 

 audible sensation in the ear, and F the corresponding force. Then 

 X2 will be the velocity of the ear drum corresponding to minimum 

 audibility in equation (2). In the calibration, the pressure P' on the 

 condenser transmitter diaphragm corresponds to Xi. The total force 

 acting on this diaphragm is p'a' where now a' designates its area. 

 Since this force is relieved by the motion of the diaphragm, it is seen 

 from equation (1) to be equal to \ 



p'a' = M'nXi. (;j) 



