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4 - The Wave Equation

Published online by Cambridge University Press:  02 April 2020

Joel Franklin
Joel Franklin
Affiliation:
Reed College, Oregon
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Summary

Taking the continuum limit of the chains of masses from the previous chapter, we arrive at the wave equation, the physical subject of this chapter.The connection to approximate string motion is an additional motivation.Viewed as a manifestation of a conservation law, the wave equation can be extended to other conservative, but nonlinear cases, like traffic flow.Mathematically, we are interested in turning partial differential equations (PDEs) into ODEs, making contact with some familiar examples.Making PDEs into ODEs occurs in a couple of ways --- the method of characteristics, and additive/multiplicative separation of variables are the primary tools.

Keywords

Balls and springsWave equationLongitudinal wavesInextensible stringStanding wavesPlane wavesDelayShocks
Type
Chapter
Information
Mathematical Methods for Oscillations and Waves , pp. 90 - 119
Publisher: Cambridge University Press
Print publication year: 2020

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  • The Wave Equation
  • Joel Franklin, Reed College, Oregon
  • Book: Mathematical Methods for Oscillations and Waves
  • Online publication: 02 April 2020
  • Chapter DOI: https://doi.org/10.1017/9781108769228.006
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  • The Wave Equation
  • Joel Franklin, Reed College, Oregon
  • Book: Mathematical Methods for Oscillations and Waves
  • Online publication: 02 April 2020
  • Chapter DOI: https://doi.org/10.1017/9781108769228.006
Available formats
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To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • The Wave Equation
  • Joel Franklin, Reed College, Oregon
  • Book: Mathematical Methods for Oscillations and Waves
  • Online publication: 02 April 2020
  • Chapter DOI: https://doi.org/10.1017/9781108769228.006
Available formats
×