TYMPANIC DISPLACEMENTS 



265 



Shape at rest 



shown in Fig. VII-5 to function. These begin to be present at about 

 2000 cycles and then again at 5000 cycles. 



The nodal circles occurring in such a narrow frequency range give 

 the conical loud speaker a more pleasant tone than a disk loud speaker. 

 If the paper cone is too stiff, however, 

 its stiffness accentuates the higher fre- 

 quencies, giving speech reproductions a 

 harsh swishing quality. 



Figure VII-5 shows the successive 

 shapes of a homogeneous loss-free coni- 

 cal shell vibrating in the first and second 

 center-moving symmetrical modes, in 

 vacuo. Note particularly that on the 

 forward thrust of the center a buckling 

 action travels down the cone. 



The response characteristics of the 



cone may be further modified by altering 



the apical angle and by adding circular 



corrugations and changing its construc- 



., . .. ,., . i . , , Fig. VII-5. The successive 



tion so that its resonance quality is highly shapeg of a vibrating conical 



damped and its upper frequencies are s h e n 

 more or less accentuated. These changes 



produce a very complex response structure whose method of vibration is 

 not completely understood. This model somewhat resembles the ear- 

 drum except that it is too symmetrical. 



If the tissue structure of the eardrum is an indication of its response 

 characteristics, the tympanum can be considered to be a shallow conical 

 membrane which through adaptation has developed a structure possess- 

 ing two nodal circles, of reinforced fibrous tissue. These allow the sur- 

 face to attain its characteristic bowed structure under tension. 



To complicate matters, the membrane is unsymmetrical in shape 

 and unsymmetrically loaded by the attached malleus. The loud speaker 

 is therefore only a very rough approximation of a very complex unsym- 

 metrically loaded membrane whose response characteristics still await 

 solution. 



Two nodal circles 



Tympanic Displacements 



The tympanic membrane according to Geffcken [1934] possesses a 

 greater relative stiffness for low frequencies than for high frequencies. 

 Bekesy's [1936] measurements show that, at a pressure of 9800 dynes/cm 2 

 and a frequency of 10 cycles, a tympanic displacement of 0.2 to 0.4 mm is 



