www.haystack.mit.edu/.../waves/General%20Wave%20Properties/General%20Wave%20Properties.ppt
(is powerpoint slide from other people who upload)

if not pleas go google
1.general wave properties
2.go to second one
3.download the power point slide


Standing Waves applet
http://www.physics.smu.edu/~olness/www/05fall1320/applet/pipe-waves.html
(can see the waves)


The wave equation
Main articles: Wave equation and D'Alembert's formula
See also: Telegrapher's equations

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).[12] General solutions are based upon Duhamel's principle.[13]

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

\frac{1}{v^2}\frac{\partial^2 u}{\partial t^2}=\frac{\partial^2 u}{\partial x^2}. \,

The velocity v will depend on the medium through which the wave is moving.

The general solution for the wave equation in one dimension was given by d'Alembert; it is known as d'Alembert's formula:[14]

u(x,t)=F(x-vt)+G(x+vt). \,

This formula represents two shapes traveling through the medium in opposite directions; F in the positive x direction, and G in the negative x direction, of arbitrary functional shapes F and G.
[edit] Spatial and temporal relationships
See also: Wavelength
Wavelength of an irregular periodic waveform at a particular moment in time based upon the crest-to-crest or trough-to-trough definition of λ.[15]

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