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A set of 55 clarinet reeds is observed by holography, collecting 2 series ofmeasurements made under 2 different moisture contents, from which the resonancefrequencies of the 15 first modes are deduced. A statistical analysis of theresults reveals good correlations, but also significant differences betweenboth series. Within a given series, flexural modes are not strongly correlated.A Principal Component Analysis (PCA) shows that the measurements of each seriescan be described with 3 factors capturing more than $90\%$ of the variance: thefirst is linked with transverse modes, the second with flexural modes of highorder and the third with the first flexural mode. A forth factor is necessaryto take into account the individual sensitivity to moisture content. Numerical3D simulations are conducted by Finite Element Method, based on a given reedshape and an orthotropic model. A sensitivity analysis revels that, besides thedensity, the theoretical frequencies depend mainly on 2 parameters: $E_L$ and$G_{LT}$. An approximate analytical formula is proposed to calculate theresonance frequencies as a function of these 2 parameters. The discrepancybetween the observed frequencies and those calculated with the analyticalformula suggests that the elastic moduli of the measured reeds are frequencydependent. A viscoelastic model is then developed, whose parameters arecomputed as a linear combination from 4 orthogonal components, using a standardleast squares fitting procedure and leading to an objective characterization ofthe material properties of the cane \textit{Arundo donax}.

Statistical Estimation of Mechanical Parameters of Clarinet Reeds Using Experimental and Numerical Approaches