Difference between revisions of "Wave Equation"
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(Created page with "Source: http://en.wikipedia.org/wiki/Wave The wave equation is a partial differential equation that describes the evolution of a wave over time in a medium where the wave pro...") |
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In particular, consider the wave equation in one dimension, for example, as applied to a string. Suppose a one-dimensional wave is traveling along the x axis with velocity v and amplitude u (which generally depends on both x and t), the wave equation is | In particular, consider the wave equation in one dimension, for example, as applied to a string. Suppose a one-dimensional wave is traveling along the x axis with velocity v and amplitude u (which generally depends on both x and t), the wave equation is | ||
| − | <math> | + | <math> \frac{1}{v^2}\frac{\partial^2 u}{\partial t^2}=\frac{\partial^2 u}{\partial x^2}. \ </math> |
The velocity v will depend on the medium through which the wave is moving. | The velocity v will depend on the medium through which the wave is moving. | ||
Latest revision as of 20:16, 27 August 2020
Source: http://en.wikipedia.org/wiki/Wave
The wave equation is a partial differential equation that describes the evolution of a wave over time in a medium where the wave propagates at the same speed independent of wavelength (no dispersion), and independent of amplitude (linear media, not nonlinear).
In particular, consider the wave equation in one dimension, for example, as applied to a string. Suppose a one-dimensional wave is traveling along the x axis with velocity v and amplitude u (which generally depends on both x and t), the wave equation is
The velocity v will depend on the medium through which the wave is moving.
See also:
Derivation of the Wave Equation
or watch:
