The Wave Equation.

Exit[]

sol = NDSolve[{
D[f[t,x],t,t]==1D[f[t,x],x,x],
f[0,x]== Sin[x],
f[t,0]==0,
f[t,2π]==0
},f,{t,0,10},{x,0,2π}][[1,1,2]]

Plot3D[sol[t,x],{t,0,10},{x,0,2π}]

Animate[Plot[sol[t,x],{x,0,2π},Filling->Axis,PlotRange->{{0,2π},{-2,2}}],{t,0,10}]