# File:Drum vibration mode21.gif

Drum_vibration_mode21.gif(248 × 130 pixels, file size: 230 KB, MIME type: image/gif, looped, 19 frames, 1.9 s)
 Description Illustration of vibrations of a drum. Date 12 January 2008, 06:21 (UTC) Source self-made with MATLAB Author Oleg Alexandrov
 This diagram was created with MATLAB.
 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)

```function main()

k = 2; % k-th asimuthal number and bessel function
p = 1; % p-th bessel root

q=find_pth_bessel_root(k, p);

N=20; % used for plotting

% Get a grid
R1=linspace(0.0, 1.0, N);
Theta1=linspace(0.0, 2*pi, N);
[R, Theta]=meshgrid(R1, Theta1);
X=R.*cos(Theta);
Y=R.*sin(Theta);

T=linspace(0.0, 2*pi/q, N); T=T(1:(N-1));

for iter=1:length(T);

t = T(iter);
Z=sin(q*t)*besselj(k, q*R).*cos(k*Theta);

figure(1); clf;
surf(X, Y, Z);
caxis([-1, 1]);
colormap autumn;

% viewing angle
view(108, 42);

axis([-1, 1, -1, 1, -1, 1]);
axis off;

H=text(0, -0.3, 1.4, sprintf('(%d, %d) mode', k, p), 'fontsize', 25);

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

pause(0.1);
end

% converted to gif with the command
% convert -antialias -loop 10000 -delay 10  -scale 50% Frame10* Drum_vibration_mode21.gif

function r = find_pth_bessel_root(k, p)

% a dummy way of finding the root, just get a small interval where the root is

X=0.5:0.5:(10*p+1); Y = besselj(k, X);
[a, b] = find_nthroot(X, Y, p);

X=a:0.01:b; Y = besselj(k, X);
[a, b] = find_nthroot(X, Y, 1);

X=a:0.0001:b; Y = besselj(k, X);
[a, b] = find_nthroot(X, Y, 1);

r=(a+b)/2;

function [a, b] = find_nthroot(X, Y, n)

l=0;

m=length(X);
for i=1:(m-1)
if ( Y(i) >= 0  & Y(i+1) <= 0 ) | ( Y(i) <= 0  & Y(i+1) >= 0 )
l=l+1;
end

if l==n
a=X(i); b=X(i+1);

%disp(sprintf('Error in finding the root %0.9g', b-a));
return;
end
end

```

## File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current04:46, 16 January 2008248 × 130 (230 KB)Oleg AlexandrovStrip caption, looks better like this
06:33, 12 January 2008250 × 168 (239 KB)Oleg Alexandrov{{Information |Description=Illustration of vibrations of a drum. |Source=self-made with MATLAB |Date=06:21, 12 January 2008 (UTC) |Author= Oleg Alexandrov |Permission= |other_versions= }} {{PD-self
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