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| View Original: | Partial transmittance.gif (367x161) | |||
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| Keywords: Partial transmittance.gif Illustration of partial reflection of a wave A gaussian wave on a one-dimensional string strikes a boundary with transmission coefficient of 0 5 Half the wave is transmitted and half is reflected Illustration de la réflection partielle d'une onde Une onde gaussienne se déplaçant sur un ressort unidimensionnel est réfléchie/transmise au niveau d'une interface avec un coefficient de transmission de 0 5 self-made with MATLAB source code below 2007-11-26 Oleg Alexandrov Created with MATLAB MATLAB source code <source lang matlab > Partial transmittance and reflectance of a wave Code is messed up don't have time to clean it now function main KSmrq's colors red 0 867 0 06 0 14; blue 0 129 205/256; green 0 200 70/256; yellow 254 194 0/256; white 0 99 1 1 1; black 0 0 0; length of the string and the grid L 5; N 151; X linspace 0 L N ; h X 2 -X 1 ; space grid size c 0 01; speed of the wave tau 0 25 h/c; time grid size form a medium with a discontinuous wave speed C 0 X+c; D L/2; c_right 0 5 c; speed to the right of the disc for i 1 N if X i > D C i c_right; end end Now C c for x < D and C c_right for x > D K 5; steepness of the bump S 0; shift the wave f inline 'exp -K x-S 2 ' 'x' 'S' 'K' ; a gaussian as an initial wave df inline '-2 K x-S exp -K x-S 2 ' 'x' 'S' 'K' ; derivative of f wave at time 0 and tau U0 0 f X S K ; U1 U0 - 2 tau c df X S K ; U 0 U0; current U plot between Start and End Start 130; End 500; hack to capture the first period of the wave min_k 2 N; k_old min_k; turn_on 0; frame_no 0; for j 1 End fixed end points U 1 0; U N 0; finite difference discretization in time for i 2 N-1 U i C i tau/h 2 U1 i+1 -2 U1 i +U1 i-1 + 2 U1 i - U0 i ; end update info for the next iteration U0 U1; U1 U; spacing 7; plot the wave if rem j spacing 1 j > Start figure 1 ; clf; hold on; axis equal; axis off; lw 3; linewidth size of the window ys 1 2; low -0 5 ys; high ys; plot D D low high 'color' black 'linewidth' 0 7 lw fill X 1 D D X 1 low low high high 0 9 1 1 'edgealpha' 0 ; fill D X N X N D low low high high 1 1 1 'edgealpha' 0 ; plot X U 'color' red 'linewidth' lw ; plot the ends of the string small_rad 0 06; axis -small_rad 0 82 L -ys ys ; small markers to keep the bounding box fixed when saving to eps plot -small_rad ys ' ' 'color' white ; plot L+small_rad -ys ' ' 'color' white ; pause 0 1 frame_no frame_no + 1; frame sprintf 'Frame d eps' 1000+frame_no ; saveas gcf frame 'psc2' ; frame sprintf 'Frame d png' 1000+frame_no ; saveas gcf frame ; disp frame print frame '-dpng' '-r300' ; end end The gif image was creating with the command convert -antialias -loop 10000 -delay 8 -compress LZW -scale 20 Frame10 png Partial_transmittance gif and was later cropped in Gimp </source> Animations of vibrations and waves Pulse physics Waves on ropes and strings Files by User Oleg Alexandrov from en wikipedia Animated GIF Animations of curves Sensory Neuroscience Hearing and speech Reflection diagrams Images with Matlab source code | ||||
