Open main menu
Home
Random
Recent changes
Special pages
Community portal
Preferences
About Wikipedia
Disclaimers
Incubator escapee wiki
Search
User menu
Talk
Dark mode
Contributions
Create account
Log in
Editing
Wave equation
(section)
Warning:
You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in
or
create an account
, your edits will be attributed to your username, along with other benefits.
Anti-spam check. Do
not
fill this in!
====Stress pulse in a bar==== In the case of a stress pulse propagating longitudinally through a bar, the bar acts much like an infinite number of springs in series and can be taken as an extension of the equation derived for Hooke's law. A uniform bar, i.e. of constant cross-section, made from a linear elastic material has a stiffness {{mvar|K}} given by <math display="block">K = \frac{EA}{L},</math> where {{mvar|A}} is the cross-sectional area, and {{mvar|E}} is the [[Young's modulus]] of the material. The wave equation becomes <math display="block">\frac{\partial^2 u(x, t)}{\partial t^2} = \frac{EAL}{M} \frac{\partial^2 u(x, t)}{\partial x^2}.</math> {{math|''AL''}} is equal to the volume of the bar, and therefore <math display="block">\frac{AL}{M} = \frac{1}{\rho},</math> where {{mvar|Ο}} is the density of the material. The wave equation reduces to <math display="block">\frac{\partial^2 u(x, t)}{\partial t^2} = \frac{E}{\rho} \frac{\partial^2 u(x, t)}{\partial x^2}.</math> The speed of a stress wave in a bar is therefore <math>\sqrt{E/\rho}</math>.
Edit summary
(Briefly describe your changes)
By publishing changes, you agree to the
Terms of Use
, and you irrevocably agree to release your contribution under the
CC BY-SA 4.0 License
and the
GFDL
. You agree that a hyperlink or URL is sufficient attribution under the Creative Commons license.
Cancel
Editing help
(opens in new window)