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Embedded SystemsFPGAElectronics

Physical Audio Signal Processing
    Elementary Physics, Mechanics, and Acoustics
       Properties of Elastic Solids
          Young's Modulus

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Young's Modulus

Young's modulus can be thought of as the spring constant for solids. Consider an ideal rod (or bar) of length $ L$ and cross-sectional area $ S$. Suppose we apply a force $ F$ to the face of area $ S$, causing a displacement $ \Delta L$ along the axis of the rod. Then Young's modulus $ Y$ is given by

$\displaystyle Y \isdefs \frac{\mbox{Stress}}{\mbox{Strain}} \isdefs \frac{F/S}{\Delta L/L} $

where

\begin{eqnarray*} F &=& \mbox{total applied force}\\ S &=& \mbox{area over whic... ...a L/L &=& \mbox{\emph{strain} = displacement per unit length}\\ \end{eqnarray*}

For wood, Young's modulus $ Y$ is on the order of $ 10$ N/m$ \null^2$. For aluminum, it is around $ 70$ (a bit higher than glass which is near $ 65$), and structural steel has $ Y\approx 200$ [180].


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Next: Young's Modulus as a Spring Constant

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.


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