64 BELL SYSTEM TECHNICAL JOURNAL 



rather indefinite. When a figure is given in ergs per second, the rate 

 of flow of energy through an area equal to that of the ear opening in 

 an unobstructed wave, is commonly meant. This has no simple 

 relation, theoretically at any rate, to the net rate of flow of energy 

 into the ear when the head is placed as an obstruction to the wave. 

 The distortion of the sound field by the head varies greatly with 

 frequency. Similarly, there is no simple relation between the energy 

 flowing into the ear and that transmitted to and absorbed by the ear 

 drum or by the cochlea. In the experiments recorded above, atten- 

 tion was paid to the experimental set-up so as to make the figures 

 given have a more definite dynamical significance. Sensitivity is 

 given in terms of the alternating (root mean square) pressure to 

 produce a minimum audible sensation. The term "pressure" has so 

 far been used in a rather loose sense. Just why this is so will be seen 

 from the following argument. 



The simplest method of describing the constants of a mechanical 

 system is in terms of the components of its mechanical impedance 

 and their relative dispositions in the same way that an electrical 

 circuit is described by giving its resistance, inductance and capacity 

 and the way in which they are connected. In a linear system having 

 a single degree of freedom, the impedance may in general be written 

 in the form 



Z = r -\- wjni -\- s/jw. 

 The symbols are as follows: 



j = V^T 



w = 27r times the frequency, 



r = frictional resistance to motion, with respect to a station- 

 ary body and involves dissipation of energy at a rate 

 of Pr where x is the root mean square value of the 

 relative velocity. The velocity x will be assumed 

 simply sinusoidal in what follows, 



ni = mass or inertia constant involving an average storage 

 kinetic energy of x^m through one cycle, 



s = stiffness constant involving an average storage of 

 potential energy through one cycle of x^s/w^. 



If the r. m. s. alternating force acting is F, the motion at any 

 frequency is given by 



X = F/Z. 



In analyzing a system in which the constants may be considered 



