Sovrapposizione di due oscillazioni armoniche con la stessa frequenza

dimimm=1000;

xmax=30;
nx=100;

k1=1;
k2=k1;
a1=1;

tmax=1000;
nt=200;
tpasso=Pi/12;

Animate[
Manipulate[
Column[
{Plot[{a1 Sin[k1 ( x-t)]},{x,-xmax,xmax},PlotRange->2,PlotStyle->{Red},AspectRatio->1/6,ImageSize->dimimm,PlotPoints->nx,
Mesh->{1},MeshStyle->{Directive[PointSize[Large],Red]}],
Plot[{a2 Sin[k2( x-t)+dfi]},{x,-xmax,xmax},PlotRange->2,PlotStyle->{Blue},AspectRatio->1/6,ImageSize->dimimm,PlotPoints->nx,
Mesh->{1},MeshStyle->{Directive[PointSize[Large],Blue]}],
Plot[{a1 Sin[k1 ( x-t)]+a2 Sin[k2 ( x-t)+dfi]},{x,-xmax,xmax},PlotStyle->{Black},PlotRange->2,AspectRatio->1/6,ImageSize->dimimm,PlotPoints->nx,Mesh->1,MeshStyle->{PointSize[Large]}]
}
],{{a2,a1,"a2/a1"},0,1},{{dfi,0,"sfasamento"},0,2 Pi,Pi/20}
],{t,0,tmax,tpasso},AnimationRate->6]

Sovrapposizione di due oscillazioni armoniche con frequenze diverse

dimimm=1000;

xmax=50;
nx=100;

tmax=1000;
nt=200;
tpasso=Pi/12;

Manipulate[Column[{Plot[{Sin[( x-t)],Sin[rk( x-t)+dfi]},{x,-xmax,xmax},PlotRange->1.1,AspectRatio->1/5,ImageSize->dimimm,PlotPoints->nx,
Mesh->0,MeshStyle->{Directive[PointSize[Small],Red],Directive[PointSize[Large],Blue]}],
Plot[{Sin[( x-t)]+Sin[rk( x-t)+dfi],2 Cos[(rk-1)((x-t))/2+dfi/2]},{x,-xmax,xmax},PlotStyle->{Black,Dashed},PlotRange->2,AspectRatio->1/5,ImageSize->dimimm,PlotPoints->nx,Mesh->0,MeshStyle->{PointSize[Small],PointSize[Large]}]}],{{rk,1},.5,1.5},{{dfi,Pi/2},0,2 Pi},{t,0,tmax,tpasso}]

dimimm=1000;

xmax=100;
nx=100;

tmax=1000;
nt=200;
tpasso=Pi/12;

Manipulate[Column[{Plot[{Sin[( x-t)],Sin[rk( x-t)+dfi]},{x,0,xmax},PlotRange->1.1,AspectRatio->1/5,ImageSize->dimimm,PlotPoints->nx,
Mesh->{1},MeshStyle->{Directive[PointSize[Large]]}],
Plot[{Sin[( x-t)]+Sin[rk( x-t)+dfi]},{x,0,xmax},PlotStyle->{Black},PlotRange->2,AspectRatio->1/5,ImageSize->dimimm,PlotPoints->nx,Mesh->1,MeshStyle->{PointSize[Large]}]}],{{rk,1},.5,1.5},{{dfi,Pi/2},0,2 Pi},{t,0,tmax,tpasso}]

f1=440;
f2=445;
forma1=Sin[2*Pi f1 t];
forma2=Sin[2*Pi f2 t];
forma3=forma1+forma2;
Play[forma1,{t,0,5}]
Play[forma2,{t,0,5}]
Play[forma3,{t,0,5}]

f1=440;
Manipulate[Play[Sin[2*Pi f1 t]+Sin[2*Pi f2 t],{t,0,4}],{{f2,f1},f1-10,f1+10}]

Sovrapposizione di due oscillazioni armoniche con la stessa frequenza contropropaganti

dimimm=1000;

xmax=8 Pi;
nx=100;

k1=1;
k2=k1;

a1=1;

tmax=1000;
nt=200;
tpasso=Pi/100;

Animate[
Manipulate[
Column[
{Plot[{a1 Cos[k1 ( x-t)]},{x,-xmax,xmax},PlotRange->2,PlotStyle->{Red},AspectRatio->1/6,ImageSize->dimimm,PlotPoints->nx,
Mesh->{1},MeshStyle->{Directive[PointSize[Large],Red]}],
Plot[{a2 Cos[k2( -x-t)+dfi]},{x,-xmax,xmax},PlotRange->2,PlotStyle->{Blue},AspectRatio->1/6,ImageSize->dimimm,PlotPoints->nx,
Mesh->{1},MeshStyle->{Directive[PointSize[Large],Blue]}],
Plot[{a1 Cos[k1 ( x-t)]+a2 Cos[k2 ( -x-t)+dfi]},{x,-xmax,xmax},PlotStyle->{Black},PlotRange->2,AspectRatio->1/6,ImageSize->dimimm,PlotPoints->nx,Mesh->1,MeshStyle->{PointSize[Large]}]
}
],{{a2,a1,"a2/a1"},0,2},{{dfi,0,"sfasamento"},0,2 Pi,Pi/20}
],{t,0,tmax,tpasso},AnimationRate->6]