GraphingCalculator 4;
Window 44 0 829 1337;
PaneDivider 298;
FontSizes 14;
Slider 0 2;
SliderControlValue 84;
2D.Scale 0.05 1 2 5;
2D.BottomLeft -14.4375 -0.146875;
2D.GraphPaper 0;
Text "<size=17>Travelling wave.

Version 0.7 4-15-11
To do:
(i)  

Define amplitude, wavelength, frequency, wave direction, wavenumber, angular frequency, and phase velocity:";
MathPaneSlider 6;
Expr A=slider([0,10,40]);
Color 4;
MathPaneSlider 4;
Expr L=slider([0,10,40]);
Color 6;
MathPaneSlider 4;
Expr f=slider([0,10,40]);
Color 5;
MathPaneSlider 1;
Expr a=slider([-1,1,1]);
Color 2;
Expr K=2*pi/L,W=2*pi*f,V_p=W/K;
Text "<size=16>Wave moving to the right (a=+1) or left (a=-1) and its transverse velocity(with scaling s to improve visibility):";
Color 3;
Expr function(Y,x,a)=A*sin([K*x-(a*W*n)]);
Color 3;
MathPaneSlider 200;
Expr s=slider([0,1]);
Color 2;
Expr function(V,x,a)=-(s*a*W*A*cos([K*x-(a*W*n)]));
Text "<size=16>With our without x>X, as needed:";
Color 3;
Expr y=function(Y,x,a),x>X;
Color 8;
Expr y=function(Y,x,a);
Text "<size=16>Unstretched string:";
Color 7;
Expr y=0;
Text "<size=16>Point on wave; window on it";
Color 4;
Expr X=slider([0,5,40]);
Color 7;
MathPaneSlider 59;
Expr h=slider([0,1]);
MathPaneSlider 16;
Expr l=slider([0,0.5]);
Expr vector(X,function(Y,X,a));
Color 17;
Expr abs(y)>A+h;
Color 17;
Expr abs(x-X)>l,abs(y)<A+h;
Text "<size=16>""History"" plot of point X.   (' x and y to get side-by-side display.) ";
Color 17;
Expr function(Y,X,a*x/n);
Color 17;
Expr vector(x,y)=vector(a*V_p*n,function(Y,X,a));
Text "<size=16>Transverse velocity (on wave, on axis, and at X):";
Color 17;
Expr vector(b,function(Y,b,a)),vector(b,function(V,b,a)+function(Y,b,a)),in(b,set(0,L/8,2*L/8,3*L/8,4*L/8,5*L/8,6*L/8,7*L/8,L));
Color 17;
Expr vector(b,0),vector(b,function(V,b,a)),in(b,set(0,L/8,2*L/8,3*L/8,4*L/8,5*L/8,6*L/8,7*L/8,L));
Color 17;
Expr y=0,0<x<L;
Color 17;
Expr vector(X,function(Y,X,a)),vector(X,function(Y,X,a)+function(V,X,a));
Text "<size=16>Wave (phase) velocity):";
Color 17;
Expr vector(a*V_p*[n+1/(4*f)],A),vector(a*V_p*[n+1/(4*f)]+V_p,A);
Text "<size=18>Sum of wave moving to left and wave moving to right is standing wave:";
Color 17;
Expr y=function(Y,x,-a);
Color 17;
Expr function(Y,x,1)+function(Y,x,-1);
Text "<size=15>Option click on slider play button to get continuous motion in one direction.


<size=14>Author: David A. Craig <<http://web.lemoyne.edu/~craigda/>";