Difference between revisions of "Wave equation"
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| − | The wave equation is an important differential | + | The '''wave equation''' is an important [[differential equation]] in [[physics]]. It describes how [[waves]] propagate through mediums, whether they be [[transverse wave]]s (e.g. [[electromagnetic radiation]]) or [[longitudinal wave]]s (e.g. [[sound]] waves). |
==One-Dimensional Wave Equation== | ==One-Dimensional Wave Equation== | ||
| − | One type of wave equation is the one-dimensional wave equation. The mathematical relation describes a wave whose parts only oscillate in ''one dimension''. This wave, however, can ''propagate'' in all three spacial dimensions. An example would be a vibrating rope or string with both ends fixed. | + | One type of wave equation is the one-dimensional wave equation. The mathematical relation describes a wave whose parts only [[oscillate]] in ''one dimension''. This wave, however, can ''propagate'' in all three spacial dimensions. An example would be a vibrating rope or string with both ends fixed. |
The one-dimensional wave equation can be written<ref>Pain, H.J. ''The Physics of Vibrations and Waves'' 6th edition. Southern Gate, Chichester, West Sussex, England: John Wiley & Sons, 2005</ref>: | The one-dimensional wave equation can be written<ref>Pain, H.J. ''The Physics of Vibrations and Waves'' 6th edition. Southern Gate, Chichester, West Sussex, England: John Wiley & Sons, 2005</ref>: | ||
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where y = y(x,t), the y-direction of motion at a point x that changes with time t, | where y = y(x,t), the y-direction of motion at a point x that changes with time t, | ||
and v = the [[phase velocity]] of the wave. | and v = the [[phase velocity]] of the wave. | ||
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==References== | ==References== | ||
| − | + | <small><references/></small> | |
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[[category:physics]] | [[category:physics]] | ||
Revision as of 09:27, March 6, 2009
The wave equation is an important differential equation in physics. It describes how waves propagate through mediums, whether they be transverse waves (e.g. electromagnetic radiation) or longitudinal waves (e.g. sound waves).
One-Dimensional Wave Equation
One type of wave equation is the one-dimensional wave equation. The mathematical relation describes a wave whose parts only oscillate in one dimension. This wave, however, can propagate in all three spacial dimensions. An example would be a vibrating rope or string with both ends fixed.
The one-dimensional wave equation can be written[1]:
<math> \frac{\partial^2 y}{dx^2} = \frac{1}{v^2} \frac{\partial^2 y}{dt^2} </math>
where y = y(x,t), the y-direction of motion at a point x that changes with time t, and v = the phase velocity of the wave.
References
- ↑ Pain, H.J. The Physics of Vibrations and Waves 6th edition. Southern Gate, Chichester, West Sussex, England: John Wiley & Sons, 2005