272 AUDITORY BIOPHYSICS 



velop in the faces of the articulation. If the malleus moves outward, 

 the center of rotation is located below the superior edge of the incus 

 (Fig. VII-7), and on inward motion of the malleus a similar center of 

 rotation is developed at a diagonally opposite point lying at the lower 

 edge of the articulating surface. The lengths of the lever arms malleus 

 to incus on outward motion are 1 to 1 ; on an inward motion, nearly 2 to 1. 

 These changes in length of the lever arms produce distortions in any 

 symmetrical alternating force applied to the end of the manubrium. 

 The degree of asymmetry depends on the rigidity of coupling of this 

 articulation. 



Coupling 



When two mechanisms are so placed or interconnected that energy- 

 may be transferred from one to the other they are said to be coupled. 



The extent to which mechanisms 

 are coupled is expressed by the 

 coupling coefficient. 



A simple piece of apparatus il- 

 lustrating the factors governing 

 the degree of coupling is shown in 

 Fig. VII-10. Fig. VII-10. It consists of two up- 



rights across the tops of which is 

 fastened a string. From the string at a and b are suspended two pen- 

 dulums A and B; their lengths are adjustable, and they can be slid 

 along the supporting string so that the points of support a and 6 can be 

 varied. 



Each of the pendulums has a natural period of its own, and as the 

 pendulum swings it tends to make the other pendulum oscillate also. If 

 A is pulled to one side, bob B being stationary, it will pull the point of 

 support, a, sidewise, and this pulls point b sidewise with it. This in- 

 duced motion of b will gradually set bob B into motion. 



The coupling of the two pendulums depends, for a given length of 

 pendulum, on the distance apart of the points of support a and b, and 

 on the tension of the supporting string. The greater the separation of a 

 and 6, the smaller is the coupling. The greater the tension in the string 

 between a and b, the smaller is the coupb'ng. In the transfer of the en- 

 ergy from A to B it can be observed that periodic variations in amplitude 

 (beats) occur unless the coupling is small and highly damped. Favorable 

 conditions for beats to develop occur with large coupling and loose con- 

 nections between a and 6. The transfer of energy from the first mech- 

 anism to the second and then back again is not marked as long as the 

 coupling is kept small. The transfer is then too slow for any appre- 

 ciable surging to take place. 



