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 Hello, Although I submitted the same question a couple of days ago here, but I am still trying to solve the 1-dim acoustic wave equation with two different media. Actually, though this equation, I want to know how much the acoustic pulse is reflected and transmitted at the interface. Could you please help me or can give some comments ? In the following code, I used the two continuity conditions of the acoustic wave at the interface of media, which are pressure and displacement continuity conditions. Thank you very much in advance. 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 continuity conditions at interface, Pressure : [Rho]1 v1^2 \ (D[u1[x,t],x]/.x->0)== [Rho]2 v2^2 (D[u2[x,t],x]/.x->0), \ Displacement : u1[0,t]==u2[0,t] *) 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] /. 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"}}][] Plot3D[u1[x, t] /. Sol, {x, -L, L}, {t, -1, T}, PlotRange -> All] Attachments: