# Natural frequencies of simplified tympanic membrane model

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## Main Question or Discussion Point

I am trying to anallytically determine natural frequencies ƒ of the tympanic membrane. I am using 2D sectorial annulus membrane as a simplified model of tympanic membrane according to following picture The parameters that i want to use are following:

THICKNESS = 0,1 mm The natural frequencies can be calculated from equation where λmn can be calculated from where Jn and Yn are Bessel functions of first kind and second kind.

I find out using MAT*AB for n=0 (zeroth order) that for m=1: λm0 = λ10=0,7484 (i used milimeters for R1 and R2)

After substituting λmn10=0,7484 into first equation for frequncy fmn i get the fundamental freq. f1=128Hz. However i am supposed to get f1=412Hz approximately. I dont know what am i doing worng. The parameters i chose are based on experiments from colleagues so i dont think they are wrong (although this tension 35MPa seems high to me)
My equations are derived using Newtons second law.
Maybe some units or dimensions in my equations are messed up?

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Andy Resnick