Waveguide
A wave is moving along the OX axis between two walls located at y
= 0, a, so that its normal modes are
u(t,x)
= A sin(n π y/a) cos(k x - ω t),
n = 1, 2, ...
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The unit time is 2π/ω.
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The unit length is a.
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Below you may choose the effective phase velocity v = ω/k,
as well as the animation step Δt.
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The upper animation shows u(t,x) for nine values
of x.
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In the lower animation you may see a contour plot of u(t,x)
(black for -A and white for A), or the instantaneous
intensity I ∝ u2, or its time average
value <I> (in the last two cases black for 0 and white for
the maximum value).
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You may also change the displayed interval 0 ≤ x ≤ xmax.
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Optionally one can see in the upper display the null values at the
selected nine points and in both displays the nodes where the wave
vanishes at all times.
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Put the mouse point over an element to get the corresponding tooltip.
Activities
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Compute the position of the nodes for mode number n.
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Use the simulation to check your calculation.
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Can you guess from the upper display of the wave values how would look
a contour plot of those values or of the instantaneous/average wave
intensity?
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Check it by selecting u(t,x) / I(t,x) / <I>!
This is an English translation of the Basque original for a course
on mechanics, oscillations and waves.
It requires Java
1.5 or newer and was created by Juan
M. Aguirregabiria with Easy
Java Simulations (Ejs) by Francisco
Esquembre. I thank Wolfgang Christian and Francisco Esquembre for
their help.