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New page: The wave equation is an important differential relationship in physics. It describes how waves propagate through mediums, whether they be [transverse waves] (e.g. electromagnetic radia...
The wave equation is an important differential relationship 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<ref>Pain, H.J. ''The Physics of Vibrations and Waves'' 6th edition. Southern Gate, Chichester, West Sussex, England: John Wiley & Sons, 2005</ref>:
<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==
<small><references/></small>
[[category:calculus]]
==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<ref>Pain, H.J. ''The Physics of Vibrations and Waves'' 6th edition. Southern Gate, Chichester, West Sussex, England: John Wiley & Sons, 2005</ref>:
<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==
<small><references/></small>
[[category:calculus]]