Young's Modulus

International Standard Book Number — Click for https://mathworld.wolfram.com/ISBN.html

Search JOS Website

JOS Home Page

JOS Online Publications

Index of terms in JOS Website

Index: Physical Audio Signal Processing

Physical Audio Signal Processing

Properties of Elastic Solids

Young's Modulus as a Spring Constant

The displacement of an object describes how far away and in what direction it has been moved, or displaced, from its rest position. Displacement is a commonly chosen wave variable in physical modeling. — Click for http://ccrma.stanford.edu/~jos/Mohonk05/Ideal_Plucked_String_Displacement.html

A force is required to change the momentum of an object. In the absence of external forces, momentum is conserved. For a mass m in flight, the momentum is m v, where v denotes the velocity of the mass. Newton's second law, F = m a, says that force equals mass times acceleration, i.e., force equals the time derivative of momentum. — Click for https://scienceworld.wolfram.com/physics/Force.html

The cross-sectional area of an oblong object is the area visible when the object is sliced transverse to its longest axis. — Click for http://en.wikipedia.org/wiki/Area

According to Hooke's law, the force F exerted by a spring stretched a distance x from its rest position is F=-kx. — Click for http://en.wikipedia.org/wiki/Spring_%28device%29

Click for http://hyperphysics.phy-astr.gsu.edu/hbase/permot3.html#c2

Search JOS Website

JOS Home Page

JOS Online Publications

Index of terms in JOS Website

Index: Physical Audio Signal Processing

Physical Audio Signal Processing

Properties of Elastic Solids

Young's Modulus as a Spring Constant

Young's Modulus

Young's modulus can be thought of as the spring constant for solids. Consider an ideal rod (or bar) of length and cross-sectional area . Suppose we apply a force to the face of area , causing a displacement $\Delta L$ along the axis of the rod. Then Young's modulus 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 is on the order of N/m $\null^2$ . For aluminum, it is around (a bit higher than glass which is near ), and structural steel has $Y\approx 200$ [181].

Subsections

Young's Modulus as a Spring Constant

[How to cite this work] [Order a printed hardcopy] [Comment on this page via email]

``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4
Copyright © 2024-06-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

Young's Modulus

``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4 Copyright © 2024-06-28 by Julius O. Smith III Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4
Copyright © 2024-06-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University