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Standing waves
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The solution to the wave equation
is of the form
but it must satisfy the conditions of free or fixed edge. In the edge case
- free wave can move but has no support so the stress and thus the deformation must be zero.
- fixed the wave cannot move but it can generate tension and with it deformation
Graphically, we have
The equation
It means that there are two solutions.
$\omega = \pm c k$
so the solution is of the form
$x_0 e^{ikx}(e^{i\omega t)}+e^{-i\omega t})$
or with Euler's relation the real part is
$2x_0 \cos(kx)\cos(\omega t)$
In other words, a function of the position oscillates in the same place without moving:
This is called a standing wave.
Las condiciones de borde permiten soluciones que tienen mas nodos como se ve en el ejemplo fijo-libre
La ecuaci n de movimiento
con la relaci n
representa la ecuaci n de onda del solido
The general solution of the wave equation
can be written in the complex space as
ID:(1888, 0)
