L=0.5;
v=275.;
t=0.;
Animate[Plot[Sum[-8L(-1)^((n+1)/2 )/(Pi^2 n^2)(Sin[n Pi/L(x-v t)]+Sin[n Pi/L(x+v t)]),{n,1,51,2}],{x,0,.5},PlotRange->{-1.0,1.0},PlotStyle->RGBColor[1,0,0]],{t,0.,.01,.0001},DefaultDuration->10]

Animate[Plot[{Sum[-L(-1)^((n+1)/2 )8/(Pi^2 n^2)Sin[n Pi/L(x-v t)],{n,1,31,2}],Sum[(-1)^((n+1)/2 +1)8/(2Pi^2 n^2)Sin[n Pi/L(x+v t)],{n,1,31,2}]},{x,0,.5},PlotRange->{-1.0,1.0},PlotStyle->{RGBColor[1,0,0],RGBColor[0,0,1]}],{t,0,.01,.0001}]

t=.;
α=5.
Animate[Plot[Sum[2 α^2 Sin[n Pi/α]/(α-1)/(2Pi^2 n^2) (Sin[n Pi/L(x-v t)]+Sin[n Pi/L(x+v t)]),{n,1,30}],{x,0,.5},PlotRange->{-1.0,1.0},PlotStyle->RGBColor[1,0,0]],{t,0,.01,.0001}]

t=.;
α=5.
Animate[Plot[{Sum[2 α^2 Sin[n Pi/α]/(α-1)/(2Pi^2 n^2) Sin[n Pi/L(x-v t)],{n,1,30}],Sum[2 α^2 Sin[n Pi/α]/(α-1)/(2Pi^2 n^2) Sin[n Pi/L(x+v t)],{n,1,30}]},{x,0,.5},PlotRange->{-1.0,1.0},PlotStyle->{RGBColor[1,0,0],RGBColor[0,0,1]}],{t,0,.01,.0001}]

t=0.;
v=275.;
L=.5;
δ=0.002
Animate[Plot[Sum[(-(-1)^((n+1)/2)/((n Pi)^2)) Sin[n Pi δ/L]2L/δ(Cos[n Pi/L (x-v t)]- Cos[n Pi/L (x+v t)]),{n,1,71,2}],{x,0,.5},PlotStyle->RGBColor[1,0,0],PlotRange->{-1.1,1.1}],{t,0.,.01,.0001},DefaultDuration->10]

t=.;
L=0.5;
v=275.;
Animate[Plot[{Sum[(-1)^((n-1)/2)/(n Pi) Cos[n Pi/L (x-v t)],{n,1,31,2}],Sum[(-1)^((n+1)/2)/(n Pi) Cos[n Pi/L (x+v t)],{n,1,31,2}]},{x,0,.5},PlotStyle->{RGBColor[1,0,0],RGBColor[0,0,1]},PlotRange->{-.5,.5}],{t,0.,.01,.0001}]

t=0.;
v=275.;
L=.5;
δ=0.002
Animate[Plot[Sum[(-(-1)^((n+1)/2)/((n Pi)^2)) Sin[n Pi δ/L]2L/δ(2 Sin[n Pi x/L] Sin[n Pi v t]),{n,1,71,2}],{x,0,.5},PlotStyle->RGBColor[1,0,0],PlotRange->{-1.1,1.1}],{t,0.,.01,.0001},DefaultDuration->10]

t=0.;
v=275.;
L=.5;
δ=0.002;
x=0.25;
Plot[Sum[(-(-1)^((n+1)/2)/((n Pi)^2)) Sin[n Pi δ/L]2L/δ(2 Sin[n Pi x/L] Sin[n Pi v t]),{n,1,51,2}],{t,0.,0.01},PlotStyle->RGBColor[1,0,0],PlotRange->{-1.1,1.1}]
Play[Sum[(-(-1)^((n+1)/2)/((n Pi)^2)) Sin[n Pi δ/L]2L/δ(2 Sin[n Pi x/L] Sin[n Pi v t]),{n,1,51,2}],{t,0.,3.0}]

t=0.;
v=275.;
L=.5;
δ=0.002;
x=0.05;
Plot[Sum[(-(-1)^((n+1)/2)/((n Pi)^2)) Sin[n Pi δ/L]2L/δ(2 Sin[n Pi x/L] Sin[n Pi v t]),{n,1,51,2}],{t,0.,0.02},PlotStyle->RGBColor[1,0,0],PlotRange->{-1.1,1.1}]
Play[Sum[(-(-1)^((n+1)/2)/((n Pi)^2)) Sin[n Pi δ/L]2L/δ(2 Sin[n Pi x/L] Sin[n Pi v t]),{n,1,51,2}],{t,0.,2.0}]

t=0.;
v=275.;
L=.5;
δ=0.002;
Plot[Sum[(-(-1)^((n+1)/2)/((n Pi)^2)) Sin[n Pi δ/L]2L/δ((4L/(n Pi)) Sin[n Pi v t]),{n,1,51,2}],{t,0.,0.01},PlotStyle->RGBColor[1,0,0],PlotRange->{-1.1,1.1}]
Play[Sum[(-(-1)^((n+1)/2)/((n Pi)^2)) Sin[n Pi δ/L]2L/δ((4L/(n Pi)) Sin[n Pi v t]),{n,1,51,2}],{t,0.,2.0}]

L=0.5;
v=275.;
t=0.;Plot[Sum[(-1)^((n+1)/2 +1)8/(2Pi^2 n^2)(Sin[n Pi/L(x-v t)]+Sin[n Pi/L(x+v t)]),{n,1,51,2}],{x,0,.5},PlotRange->{-1.0,1.0},PlotStyle->RGBColor[1,0,0]]

x=0.25;
Plot[Sum[(-1)^((n+1)/2 +1)8/(2Pi^2 n^2)2(Sin[n Pi x/L]Cos[n Pi v t/L]),{n,1,51,2}],{t,0,.01},PlotRange->{-1.0,1.0}]
Play[Sum[(-1)^((n+1)/2 +1)8/(2Pi^2 n^2)2(Sin[n Pi x/L]Cos[n Pi v t/L]),{n,1,51,2}],{t,0,3.0}]

x=0.05;
Plot[Sum[(-1)^((n+1)/2 +1)8/(2Pi^2 n^2)2(Sin[n Pi x/L]Cos[n Pi v t/L]),{n,1,51,2}],{t,0,.01},PlotRange->{-1.0,1.0}]
Play[Sum[(-1)^((n+1)/2 +1)8/(2Pi^2 n^2)2(Sin[n Pi x/L]Cos[n Pi v t/L]),{n,1,51,2}],{t,0,3.0}]

Plot[Sum[(-1)^((n+1)/2 +1)8/(2Pi^2 n^2)((4L/(n Pi))Cos[n Pi v t/L]),{n,1,51,2}],{t,0,.01}]
Play[Sum[(-1)^((n+1)/2 +1)8/(2Pi^2 n^2)((4L/(n Pi))Cos[n Pi v t/L]),{n,1,51,2}],{t,0,3.0}]

t=0.;
L=0.5;
α=0.1;
v=275.0;
x=α L;
(Subscript[y, 0])=0.1;
Plot[Sum[(-2(Subscript[y, 0])/((Pi n)^2)/(α(1-α)))Sin[n Pi x/L]Sin[n Pi v t/L],{n,1,50}],{t,0.,0.01},PlotStyle->RGBColor[1,0,0],PlotRange->{-0.5,0.5}]
Animate[Plot[Sum[(-2(Subscript[y, 0])/((Pi n)^2)/(α(1-α)))Sin[n Pi x/L]Sin[n Pi v t/L],{n,1,50}],{x,0.,0.5},PlotStyle->RGBColor[1,0,0],PlotRange->{-0.5,0.5}]
,{t,0.,0.01,0.0001}]

t=0.;
L=0.5;
α=0.1;
v=275.0;
x=α L;
(Subscript[y, 0])=0.1;
Play[Sum[(-2(Subscript[y, 0])/((Pi n)^2)/(α(1-α)))Sin[n Pi x/L]Sin[n Pi v t/L],{n,1,50}],{t,0.,2.0}]