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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 which force is applied}\\
F/S &=& \mbox{\emph{stress} = force per unit area}\\
L &=& \mbox{rest length}\\
\Delta L &=& \mbox{displacement}\\
\Delta 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$ [181].



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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2014-03-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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