Difference between revisions of "Wave equation"
(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...) |
|||
| Line 16: | Line 16: | ||
| − | [[category: | + | [[category:physics]] |
Revision as of 03:20, March 5, 2009
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[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