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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).

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>:

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.

==References==

==References==

    <small><references/></small>  

<small><references/></small>  

 

[[category:physics]]

[[category:physics]]