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| Keywords: Wave equation 1D fixed endpoints.gif Illustration of solution of one-dimensional wave equation a gaussian wave on a string fixed at both ends The wave reflects from each end with a 180° phase shift self-made with en Matlab 01 27 24 August 2007 UTC Oleg Alexandrov Created with MATLAB MATLAB source code <source lang matlab > A wave travelling on a string with fixed endpoints 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; 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 5; speed of the wave tau 0 25 h/c; time grid size 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 Big 10000; Ut zeros Big N ; Ut 1 U0; Ut 2 U1; hack to capture the first period of the wave min_k 2 N; k_old min_k; turn_on 0; for j 3 Big last_j j; fixed end points U 1 0; U N 0; finite difference discretization in time for i 2 N-1 U i c tau/h 2 U1 i+1 -2 U1 i +U1 i-1 + 2 U1 i - U0 i ; end Ut j U; update info for the next iteration U0 U1; U1 U; hack to capture the first period of the wave k find abs U max abs U ; k k 1 ; if k > N/2 turn_on 1; end min_k min min_k k_old ; if k > min_k min_k k_old turn_on 1 break; end k_old k; end truncate to the first period last_j last_j - 1; Ut Ut 1 last_j ; shift the wave by a certain amount shift floor last_j/4 ; Vt Ut; Ut last_j-shift+1 last_j Vt 1 shift ; Ut 1 last_j-shift Vt shift+1 last_j ; num_frames 100; spacing floor last_j/num_frames plot the wave for j 1 last_j-spacing+1 U Ut j ; if rem j spacing 1 figure 1 ; clf; hold on; axis equal; axis off; lw 3; linewidth plot X U 'color' red 'linewidth' lw ; plot the ends of the string small_rad 0 06; ball 0 0 small_rad red ; ball L 0 small_rad red ; size of the window ys 1 1; axis -small_rad L+small_rad -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 ; frame_no floor j/spacing +1; frame sprintf 'Frame d eps' 1000+frame_no ; disp frame saveas gcf frame 'psc2' ; end end function ball x y radius color draw a ball of given uniform color Theta 0 0 1 2 pi; X radius cos Theta +x; Y radius sin Theta +y; H fill X Y color ; set H 'EdgeColor' color ; The gif image was creating with the command convert -antialias -loop 10000 -delay 15 -compress LZW Frame10 Movie gif </source> Waves on ropes and strings Files by User Oleg Alexandrov from en wikipedia Animations of vibrations and waves Pulse physics Animated GIF Animations of curves Images with Matlab source code | ||||
