MODELS FOR SPECIFIC NERVES FOR SPECIFIC FREQUENCIES 47 



the synapse. The events at the synapse by themselves show some of the 

 limitations involved. The law of diffusion is, approximately, 



x 2 ~ Dt, 



where x is the distance diffused by a substance in time t if D is the 

 diffusion coefficient. Putting in typical numbers for the acetylcholine 

 molecule (shown to be involved in many synaptic transmissions) t turns 

 out to be about one millisecond. Thus if a second impulse were to arrive 

 at the synapse during this time, the impulses would be blended together. 

 Therefore we can estimate an upper limit of 1000 cycles/sec for the 

 transmission frequency of nerves. Experimental measurements have 

 shown that this is indeed a good estimate, and that most nerve fibers 

 can transmit only up to a few hundred cycles per second. If this limit 

 holds for the auditory nerve, then it is clear that the nerve cannot trans- 

 mit input frequencies of up to 15,000 cycles/sec, which is roughly the 

 highest frequency that adults can hear. Accordingly, the early studies 

 of the hearing mechanism focused on the finding of individual nerve 

 fibers which responded characteristically to single frequencies. Several 

 of the models proposed will now be examined briefly. 



MODELS FOR SPECIFIC NERVES FOR SPECIFIC FREQUENCIES 



There are two kinds of models which have been envisaged. The first 

 proposes that certain nerves respond to certain frequencies, due to some 

 as yet unknown mechanism. The second proposes that the nerves which 

 respond to certain frequencies do so because they are connected to other 

 elements which themselves respond to the frequencies; the nerves them- 

 selves could transmit any frequency up to their maximum. In the latter 

 category are all the so-called resonance models, which propose, for 

 example, that there are resonating structural fibers in the ear which 

 respond only to characteristic frequencies. When these structural fibers 

 oscillate, they trigger the nerve fibers to which they are connected. 

 Proponents of the resonance theories have then had to demonstrate the 

 existence of such resonating structures in the ear. 



To proceed further, we need a sketch of the relevant portions of the 

 ear. Figure 21(a) is a diagram of the snail-like cochlea. Part (b) is a 

 section of the cochlea, showing its division into three so-called canals 

 and the place of insertion of the nerve fiber into the basilar membrane. 



The eardrum is connected by means of three auditory bones (malleus, 

 incus, and stapes) to the vestibular canal. The approximate area of the 

 stapes connection is also indicated in part (b) of the figure. Thus vibra- 

 tions of the eardrum are communicated to the bones of the inner ear. 



