Sorry for the inconvenience.

Here is the code. Of you can download the attachments Thank you for the help. Really.

Remove["Global`*"];
L=10.0;T=3.0; (* L : boundary, T : time *)
\[Rho]1=5;\[Rho]2=4;  (* mass density of each layer *)
v1=5;v2=4;  (* speed of sound of each layer *)

(* For interface conditions, Pressure : \[Rho]1 v1^2 (D[u1[x,t],x]/.x->0)== \[Rho]2 v2^2 (D[u2[x,t],x]/.x->0), Velocity : (D[u1[x,t],t]/.x->0)==(D[u2[x,t],t]/.x->0) *)

Sol=NDSolve[{D[u1[x,t],t,t]== v1^2 D[u1[x,t],x,x],D[u2[x,t],t,t]== v2^2 D[u2[x,t],x,x],(D[u1[x,t],x]/.x->L)==0,(D[u2[x,t],x]/.x->-L)==0,\[Rho]1 v1^2 (D[u1[x,t],x]/.x->0)== \[Rho]2 v2^2 (D[u2[x,t],x]/.x->0),(D[u1[x,t],t]/.x->0)==(D[u2[x,t],t]/.x->0),(D[u1[x,t],t]/.t->-1)==0,(D[u2[x,t],t]/.t->-1)==0,u1[x,-1]==Exp[-20 (x-L/2)^2],u2[x,-1]==0},{u1,u2},{x,-L,L},{t,-1,T},MaxSteps->Infinity,Method->{"MethodOfLines","SpatialDiscretization"->{"TensorProductGrid"}}][[1]]
Plot3D[u1[x,t]/.Sol,{x,-L,L},{t,-1,T},PlotRange->All]