Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Wave second order derivative equation

  1. Feb 7, 2015 #1
    Whenever the second order derivative of any physical quantity is related to its second order space derivative a wave of some sort must travel in a medium, why this is so?
     
  2. jcsd
  3. Feb 7, 2015 #2

    blue_leaf77

    User Avatar
    Science Advisor
    Homework Helper

    Evanescent wave which does not propagate also satisfies wave equation.
     
  4. Feb 7, 2015 #3

    Vanadium 50

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor

    It's not so.

    [tex]\frac{\partial^2 u}{\partial t^2} = v^2 \nabla^2 u[/tex]

    is a wave, but

    [tex]\frac{\partial^2 u}{\partial t^2} = -v^2 \nabla^2 u[/tex]

    is not. The solution of the top equation is in sines and cosines, and the second is sinh and cosh.
     
  5. Feb 8, 2015 #4
    Thanks.
     
  6. Feb 8, 2015 #5
    And this is just for a linear relation. They can be "related" in more complicated ways.
    Generalizations are tricky.:)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Wave second order derivative equation
Loading...