Wave on a 2D plane
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From: igor b. on 21 Apr 2010 16:37 Hi to all! I'm trying to model and animate waves on a 2D plane (something like Rectangular Membrane Waves applet on [1]). I used expressions from [2] to do it (equation 17 is wave equation and equations 32 and 33 are used to calculate Apq and Bpq). I am trying to draw response to impulse delta(x-x0)*delta(y-y0)*delta(t) so I plugged it into equations 32 and 33 to calculate Apq and Bpq (I took that delta(0)=1 and delta'(0)=0, so Bpq then becomes 0), but when I draw it I get a lot of 'ripples' on waves (image [4]) instead of clean concentric waves (p and q go up to 10). Image [3] is the first frame at t=0. I presume that ripples are consequence of that other small waves on the first frame. For A(p,q) calculated in this way I get: A(p,q)= [ 400 0 -400 0 400 0 -400 0 ... ; 0 0 0 0 0 0 0 0 ... ; -400 0 400 0 -400 0 400 0 ... ; 0 0 0 0 0 0 0 0 ... ; . . . ] Do you have any idea of what I'm doing wrong or how to fix it? [1]http://www.falstad.com/mathphysics.html [2] http://mathworld.wolfram.com/WaveEquationRectangle.html [3] http://i44.tinypic.com/67tw7l.png [4] http://i41.tinypic.com/2ch42g7.png Cheers! Igor
From: BURT on 21 Apr 2010 16:42 On Apr 21, 1:37 pm, "igor b." <i...(a)REMOVEhyperglitch.com> wrote: > Hi to all! > > I'm trying to model and animate waves on a 2D plane (something like > Rectangular Membrane Waves applet on [1]). I used expressions from [2] > to do it (equation 17 is wave equation and equations 32 and 33 are used > to calculate Apq and Bpq). > > I am trying to draw response to impulse delta(x-x0)*delta(y-y0)*delta(t) > so I plugged it into equations 32 and 33 to calculate Apq and Bpq (I > took that delta(0)=1 and delta'(0)=0, so Bpq then becomes 0), but when I > draw it I get a lot of 'ripples' on waves (image [4]) instead of clean > concentric waves (p and q go up to 10). Image [3] is the first frame at > t=0. I presume that ripples are consequence of that other small waves on > the first frame. > > For A(p,q) calculated in this way I get: > > A(p,q)= [ 400 0 -400 0 400 0 -400 0 ... ; > 0 0 0 0 0 0 0 0 ... ; > -400 0 400 0 -400 0 400 0 ... ; > 0 0 0 0 0 0 0 0 ... ; > . > . > . > ] > > Do you have any idea of what I'm doing wrong or how to fix it? > > [1]http://www.falstad.com/mathphysics.html > [2]http://mathworld.wolfram.com/WaveEquationRectangle.html > [3]http://i44.tinypic.com/67tw7l.png > [4]http://i41.tinypic.com/2ch42g7.png > > Cheers! > Igor A light wave and a quantum wave are 3 dimensional.
From: Androcles on 21 Apr 2010 17:02
"igor b." <igor(a)REMOVEhyperglitch.com> wrote in message news:hqnnmr$l59$1(a)ss408.t-com.hr... > Hi to all! > > I'm trying to model and animate waves on a 2D plane (something like > Rectangular Membrane Waves applet on [1]). I used expressions from [2] to > do it (equation 17 is wave equation and equations 32 and 33 are used to > calculate Apq and Bpq). > > I am trying to draw response to impulse delta(x-x0)*delta(y-y0)*delta(t) > so I plugged it into equations 32 and 33 to calculate Apq and Bpq (I took > that delta(0)=1 and delta'(0)=0, so Bpq then becomes 0), but when I draw > it I get a lot of 'ripples' on waves (image [4]) instead of clean > concentric waves (p and q go up to 10). Image [3] is the first frame at > t=0. I presume that ripples are consequence of that other small waves on > the first frame. > > For A(p,q) calculated in this way I get: > > A(p,q)= [ 400 0 -400 0 400 0 -400 0 ... ; > 0 0 0 0 0 0 0 0 ... ; > -400 0 400 0 -400 0 400 0 ... ; > 0 0 0 0 0 0 0 0 ... ; > . > . > . > ] > > Do you have any idea of what I'm doing wrong or how to fix it? > > [1]http://www.falstad.com/mathphysics.html > [2] http://mathworld.wolfram.com/WaveEquationRectangle.html > [3] http://i44.tinypic.com/67tw7l.png > [4] http://i41.tinypic.com/2ch42g7.png > > Cheers! > Igor Ok, it's pretty clear from your image [3] (the first frame at t =0), that you have a bias or preference in the x and y axes which are orthogonal to the rectangle. What are all those zeroes doing in A(p,q)? Try starting with a flat surface and see what happens with just one node high. |