Difference between revisions of "Category:Simple Linear Waves"
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== Introduction == | == Introduction == | ||
| − | The principle topic of this wiki is linear water waves, however other simpler linear wave systems are discussed in some detail, especially as they relate to water wave problems. The problem on waves on a string of variable density is closely related to [[Category:Shallow | + | The principle topic of this wiki is linear water waves, however other simpler linear wave systems are discussed in some detail, especially as they relate to water wave problems. The problem on waves on a string of variable density is closely related to [[Category:Shallow Depth|Shallow Depth]] water wave equation and is discussed in detail in [[Variable Depth Shallow Water Wave Equation]]. |
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| + | == Waves on a variable density string / waves on variable depth shallow water == | ||
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| + | The equation is | ||
| + | {{shallow depth one dimension}} | ||
| + | |||
| + | |||
| + | We begin with | ||
Revision as of 23:26, 22 March 2009
Introduction
The principle topic of this wiki is linear water waves, however other simpler linear wave systems are discussed in some detail, especially as they relate to water wave problems. The problem on waves on a string of variable density is closely related to water wave equation and is discussed in detail in Variable Depth Shallow Water Wave Equation.
Waves on a variable density string / waves on variable depth shallow water
The equation is
subject to the initial conditions
where [math]\displaystyle{ \zeta }[/math] is the displacement, [math]\displaystyle{ \rho }[/math] is the string density and [math]\displaystyle{ h(x) }[/math] is the variable depth (note that we are unifying the variable density string and the wave equation in variable depth because the mathematical treatment is identical).
We begin with
Pages in category "Simple Linear Waves"
The following 3 pages are in this category, out of 3 total.
