f[x_]:=Piecewise[{{Sin[x],x>0}},0]
n=20;
f1=Join[{f[t-z]},Table[If[k==0,R12,(((R12^2)-1)/R12)(((-R23 R12))^k)]f[t-(2k d+2(Subscript[d, 1])-z)],{k,0,n}]];
f1s={f[t-z],Sum[If[k==0,R12,(((R12^2)-1)/R12)(((-R23 R12))^k)]f[t-(2k d+2(Subscript[d, 1])-z)],{k,0,n}]};
f1ss=f[t-z]+Sum[If[k==0,R12,(((R12^2)-1)/R12)(((-R23 R12))^k)]f[t-(2k d+2(Subscript[d, 1])-z)],{k,0,n}];
f2=Join[
Table[(1+R12)(((-R12 R23))^k)f[t-(z+2k d)],{k,0,n}],
Table[(1+R12)R23(((-R12 R23))^k)f[t-(2k d+2(Subscript[d, 2])-z)],{k,0,n}]
];
f2s={Sum[(1+R12)(((-R12 R23))^k)f[t-(z+2k d)],{k,0,n}],Sum[(1+R12)R23(((-R12 R23))^k)f[t-(2k d+2(Subscript[d, 2])-z)],{k,0,n}]};
f2ss=Sum[(1+R12)(((-R12 R23))^k)f[t-(z+2k d)],{k,0,n}]+Sum[(1+R12)R23(((-R12 R23))^k)f[t-(2k d+2(Subscript[d, 2])-z)],{k,0,n}];
f3=Table[(1+R12)(1+R23)(((-R12 R23))^k)f[t-(2k d+z)],{k,0,n}];
f3s=Sum[(1+R12)(1+R23)(((-R12 R23))^k)f[t-(2k d+z)],{k,0,n}];

Manipulate[
Animate[
Show[{
Plot[Evaluate[f1/.{R12->mR12,R23->mR23,d->d2-d1,(Subscript[d, 1])->d1,(Subscript[d, 2])->d2,t->tt}],{z,0,d1},PlotRange->{{0,30},{-1,1}}],
Plot[Evaluate[f2/.{R12->mR12,R23->mR23,d->d2-d1,(Subscript[d, 1])->d1,(Subscript[d, 2])->d2,t->tt}],{z,d1,d2},PlotRange->{-1,1}],
Plot[Evaluate[f3/.{R12->mR12,R23->mR23,d->d2-d1,(Subscript[d, 1])->d1,(Subscript[d, 2])->d2,t->tt}],{z,d2,30},PlotRange->{-1,1}],
Graphics[{Line[{{d1,-1.},{d1,1.}}],Line[{{d2,-1.},{d2,1.}}]}]
}],
{{tt,-1,Dynamic["t = "<>ToString[Round[tt,0.1]]]},-1,150},ControlPlacement->Top,AnimationRunning->False],
{{mR12,-0.4,Dynamic["(Subscript[R, 12]) = "<>ToString[Round[mR12,0.01]]]},-1,1},{{mR23,-0.4,Dynamic["(Subscript[R, 23]) = "<>ToString[Round[mR23,0.01]]]},-1,1},{{d1,10,Dynamic["(Subscript[d, 1]) = "<>ToString[Round[d1,0.1]]]},0,20},{{d2,20,Dynamic["(Subscript[d, 2]) = "<>ToString[Round[d2,0.1]]]},d1,30},SaveDefinitions->True]

Pomocné:

Animate[
Plot[Evaluate[{
Piecewise[{{f[t-z],z<d1},{(1+R12) f[t-z],d1≤z<d2}},(1+R12)(1+ R23) f[t-z]],
Piecewise[{{R12 f[t-(2d1-z)],z<d1},{(1+R12) f[t-z],d1≤z<d2}},(1+R12)(1+ R23) f[t-z]]
}/.{R12->-0.5,R23->-0.5,d1->10,d2->20}]
,{z,0,30},PlotRange->{-1,1}],
{t,-1,50},ControlPlacement->Top,AnimationRunning->False]