Drum_vibration_mode12.gif
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| Description | Illustration of vibrations of a drum . | |||
| Date | (UTC) | |||
| Source | self-made with MATLAB | |||
| Author | Oleg Alexandrov | |||
| Other versions |
Derivative works of this file:
File:Harmonic partials on strings.svg → File:Drum vibration mode12.gif In general, it is better to use a good SVG version. |
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 VibratingDrum()
k = 1; % k-th asimuthal number and bessel function
p = 2; % 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])
shading faceted
colormap autumn
% viewing angle
view(108, 42)
axis([-1, 1, -1, 1, -1, 1])
axis off
% To save as a GIF comment out the next the 3 lines
% file=sprintf('Frame%d.png', 1000+iter);
% fprintf('Saving to %s\n', file)
% print('-dpng', '-opengl', '-r100', file);
pause(0.01)
end
end
% converted to gif with the command (run in command shell)
% convert -antialias -loop 10000 -delay 10 -scale 50% Frame10* Drum_vibration_mode12.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;
end
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
disp('Root not found!')
end