254 AUDITORY BIOPHYSICS 



large number of suspensory ligaments, a spirally converging fluid canal 

 encased in a bony cochlea, and a complex set of end organs of the 

 acoustic nerve located in the aural membrane immersed in this fluid. 

 These end organs are stimulated by the hydrodynamic disturbances of 

 the cochlea fluids to initiate the nerve impulses which are propagated to 

 the brain via the acoustic nerve. 



The Acoustic Object Space 



The eardrum is in contact with the air in which the human ear is nor- 

 mally immersed. The eardrum can move in and out as the result of 

 pressure changes of the air in contact with its free faces. 



An observer possessing normal ears placed in this object space experi- 

 ences a sensation called a tone if the pressure disturbances at the ear- 

 drum are adequate and are repeated with a frequency of not less than 20 

 or more than 20,000 cycles per second. 



This frequency range is presented to the ear in the form of longitudinal 

 waves in the medium in contact with the eardrum. These longitudinal 

 waves are basically the results of particles executing simple harmonic 

 motions as an elastic medium. The acoustic intensity, or the energy per 

 second that flows across each square centimeter of this medium, must be 

 determined in order to evaluate the sensitivity range of the aural 

 mechanism. 



Simple Harmonic Motion 



If a small body were rotating with uniform speed in a horizontal 

 circle, and you were to elevate the plane of the circle to the level of your 

 eyes, you would see the body as if it were executing a sweep motion. 

 The length of the sweep is equal to the diameter of the circle. 



This will be called the " reference circle," and the sweep motion is its 

 projected uniform circular motion on the diameter of the reference circle, 

 designated as simple harmonic motion. 



The velocity with which a point moves, in simple harmonic motion, is 

 constantly changing in magnitude and direction. Its velocity at the 

 two ends of its sweep is zero. As the particle attains its mid or equilib- 

 rium point from either direction, it has its greatest velocity. A corre- 

 sponding acceleration is apparent. At its midpoint its acceleration is 

 zero, and at the points of maximum displacement its acceleration is 

 maximal. 



Simple harmonic motion is described very accurately by stating that 

 the restoring force is proportional to the displacement and that they are 

 always opposite in direction. 



