# Animations

## Réflexion d'une onde progressive plane

onde.mp
%@AUTEUR: Maxime Chupin
%@DATE: 11 mars 2008

verbatimtex
%&latex
\documentclass{article}
\usepackage[latin1]{inputenc}
\usepackage[garamond]{mathdesign}
\usepackage[frenchb]{babel}
\begin{document}
etex

u:=2cm;
w:=4;
k:=2;
Pi := 3.14159265;
%les cos et sin en radians
vardef sin(expr a) = sind(a/Pi*180) enddef;
vardef cos(expr a) = cosd(a/Pi*180) enddef;
% === Pointer les points avec une couleur cerclée de noir (Jean-Michel Sarlat)
def pointe(expr p,c) =
fill fullcircle scaled 4 shifted p withcolor black;
fill fullcircle scaled 3 shifted p withcolor c;
enddef;

%Macro pour hachurer (Christophe Poulain)
%===================================================================================
vardef hachurage(expr chemin, angle, ecart, trace)suffix couleur =
save $; picture$;
path support;
support=(((-37cm,0))--((37cm,0))) rotated angle;
if trace=1:
drawoptions(dashed evenly);
elseif trace=2:
drawoptions(dashed dashpattern(on12bp off6bp on3bp off6bp));
fi;
$= image( for j=-200 upto 200: if ((support shifted (ecart*j*(1,0))) intersectiontimes chemin)<>(-1,-1): draw support shifted (ecart*j*(1,0)) withcolor if str couleur="":(0,0,0) else:couleur fi; fi endfor; ); clip$ to chemin;
drawoptions();
$enddef; %=================================================================================== for t:=0 upto (12*22): beginfig(t); drawarrow (-0.5u,0)--(9u,0); drawarrow (0,-2u)--(0,2u); path ondei, onder, ondesta ,mur; for l:=0 upto 400: if l=0: ondei:=(l/50*u, cos(w*t/50-l/50*k)*u); onder:=(l/50*u, -cos(w*t/50+l/50*k)*u); ondesta:=(l/50*u,(cos(w*t/50-l/50*k)-cos(w*t/50+l/50*k))*u); else : ondei:=ondei--(l/50*u, cos(w*t/50-l/50*k)*u); onder:=onder--(l/50*u, -cos(w*t/50+l/50*k)*u); ondesta:=ondesta--(l/50*u,(cos(w*t/50-l/50*k)-cos(w*t/50+l/50*k))*u); fi; endfor; draw ondei withpen pencircle scaled 0.8pt withcolor blue; draw onder withpen pencircle scaled 0.8pt withcolor green; draw ondesta withpen pencircle scaled 1pt withcolor red; for i:=0 upto 5: pointe((2*i*Pi/4*u,0), white); endfor; mur:= (8u,2u)--(8.5u,2u)--(8.5u,-2u)--(8u,-2u)--cycle; draw hachurage(mur,45,2mm,0)red; draw mur; label.bot(btex$x$etex, (8.8u,0)); label.rt(btex$y$etex, (0,1.7u)); label.top(btex \fbox{Réflexion d'une onde progressive plane monochromatique sur un conducteur métallique} etex, (4u,2u)); label.rt(btex Onde incidente :$\vec{E}_{i}=E_{0}\cos(\omega{}t-kx)\vec{u}_{y}$etex, (3u, -2.2u)); draw (2.7u,-2.2u)--(2.9u,-2.2u) withpen pencircle scaled 0.8pt withcolor blue; label.rt(btex Onde réfléchie :$\vec{E}_{r}=-E_{0}\cos(\omega{}t+kx)\vec{u}_{y}$etex, (3u, -2.5u)); draw (2.7u,-2.5u)--(2.9u,-2.5u) withpen pencircle scaled 0.8pt withcolor green; label.rt(btex Onde \emph{stationnaire} :$\vec{E}_{s}=\vec{E}_{i}+\vec{E}_{r}=2E_{0}\sin(kx)\sin(\omega{}t)\$ etex, (3u, -2.8u));
draw (2.7u,-2.8u)--(2.9u,-2.8u) withpen pencircle scaled 1pt withcolor red;
label.rt(btex \og{}N\oe{}ux\fg{} de vibration etex, (3u,-3.1u));
pointe((2.8u,-3.1u),white);
endfig;
endfor;
end.