Category:Simple Linear Waves

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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.

Waves on a variable density string / waves on variable depth shallow water

The equation is

[math]\displaystyle{ \rho(x)\partial_t^2 \zeta = \partial_x \left(h(x) \partial_x \zeta \right). }[/math]

subject to the initial conditions

[math]\displaystyle{ \zeta_{t=0} = \zeta_0(x)\,\,\,{\rm and}\,\,\, \partial_t\zeta_{t=0} = \partial_t\zeta_0(x) }[/math]

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.