File:Two dim standing wave.gif

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Two_dim_standing_wave.gif(200 × 140 pixels, file size: 142 KB, MIME type: image/gif, looped, 10 frames, 2.0 s)

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Description

Illustration of a standing wave in a cavity resonator. Mathematically, this also represents a vibration mode of a rectangular drum or membrane.

Date (UTC)
Source self-made with MATLAB
Author Oleg Alexandrov
Matlab Logo.png
This diagram was created with MATLAB.
Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

Source code (MATLAB)[edit]

% illustration of a standing wave in two dimensions

% box size
Lx = 3; 
Ly = 4; 

h= 0.1; % grid size
[X, Y] = meshgrid(0:h:Lx, 0:h:Ly);

numP_x = 2; numP_y = 3; % number of peaks in x and y

Z=0.5*sin(2*pi*numP_x*X/Lx).*sin(2*pi*numP_y*Y/Ly);

% normalize from 0 to scale
scale = 0.5;
%Z = Z - min(min(Z));
%Z = Z/max(max(Z));

M=11;
T=linspace(0.0, 2*pi, M); T=T(1:(M-1)); T = T + 0.5*pi/(M-1);
shift = 1;

for p=1:1
   for iter=1:length(T)

      %figure(1); clf; hold on;

      t = T(iter);

      figure(1); clf;  hold on;
      surf(X, Y, Z*cos(t));
      caxis([-1, 1]);
      shading faceted;
      colormap autumn;

      
      axis equal; axis off;
      axis([0, Lx, 0, Ly, -1, 1]);

      % viewing angle
      view(38, 42);

      %H=text(0, -0.3, 1.4, sprintf('(%d, %d) mode', k, p), 'fontsize', 25);
      %image(scale*((Z*sin(t)+shift)));
      %axis equal; axis xy;
      %axis off;

      file=sprintf('Frame%d.png', 1000+iter);
      disp(sprintf('Saving to %s', file));
      print('-dpng',  '-zbuffer',  '-r100', file);
      pause(0.2);
      
   end

end

% saved to gif with the command
% convert -density 100 -loop 1000 -delay 20 Frame1* Two_dim_standing_wave.gif
% then cropped and scaled in Gimp.

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Date/TimeThumbnailDimensionsUserComment
current05:37, 16 January 2008Thumbnail for version as of 05:37, 16 January 2008200 × 140 (142 KB)Oleg Alexandrov (talk | contribs){{Information |Description=Illustration of a standing wave in a cavity resonator. Mathematically, this also represents a vibration mode of a of a rectangular drum or [[:en:membr
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