τ = -1.5;  c = 1;  ρ = 1;
f[x_] := 3*Sin[x]; 
    2  π ≤ x ≤ 3  π;
f[x_] := 
        0 /; (x > 3  π || x < 2  π);
r[t_] := 0 /; t < 1;
r[t_] := (ρ*c*f[c*t])/(2*ρ*c - τ) /; 
          t ≥ 1;
u1[x_] := 
      If[(0 ≤ x && x - t ≥ 0), 
        1/2 (f[x + c*t] + f[x - c*t]), 0]
u2[x_] := 
        If[(0 ≤ x && x - t ≤ 0), 
          1/2 (f[x + c*t] - f[-x + c*t]) + r[t - x/c], 
          0];
u3[x_] := 
      If[(0 ≥ x && x + t ≥ 0), r[t + x], 
        0]
g[x_] := 
        Plot[u1[x] + u2[x] + u3[x], {x, -15, 15}, 
          PlotRange -> {{0, 15}, {-1.1, 1.1}}, 
          DisplayFunction -> Identity];
D1[t_] := 
      Show[Graphics[{RGBColor[0, 0, 1], Thickness[0.007], 
            Line[{{0. , -4.9}, {0. , r[t]}}]}], 
        DisplayFunction -> Identity]
D2[t_] := 
      Show[Graphics[{RGBColor[0, 1, 1], 
            Polygon[{{-0.4, -3.0 + r[t]}, {0.4, -3.0 + 
                    r[t]}, {0.4, -4.7}, {-0.4, -4.7}}]}], 
        DisplayFunction -> Identity]
D3[t_] := 
      Show[Graphics[{RGBColor[0, 0, 1], Thickness[0.015], 
            Line[{{-0.4, -3.0 + r[t]}, {0.4, -3.0 + r[t]}}]}], 
        DisplayFunction -> Identity]
D4 = 
      Show[Graphics[{RGBColor[0, 0, 1], Thickness[0.007], 
            Line[{{-0.4, -1.5}, {-0.4, -4.7}}]}], 
        DisplayFunction -> Identity]
D5 = 
      Show[Graphics[{RGBColor[0, 0, 1], Thickness[0.007], 
            Line[{{-0.4, -4.7}, {0.4, -4.7}}]}], 
        DisplayFunction -> Identity]
D6 := 
      Show[Graphics[{RGBColor[0, 0, 1], Thickness[0.007], 
            Line[{{0.4, -4.7}, {0.4, -1.5}}]}], 
        DisplayFunction -> 
          Identity]

Table[
      Show[g[x], D1[t], D2[t], D3[t], D4, D5, D6, 
        PlotRange -> {{-15, 15}, {-6, 6}}, 
        DisplayFunction -> $DisplayFunction], {t, 0, 
        20,  .5}]

{⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,ϑ⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃,⁃  Graphics  ⁃}

Clear[τ, ρ, c, f, r, u1, u2, u3]
τ = 0;  c = 1;  ρ = 1;
f[x_] := 3*Sin[x]; 
    2  π ≤ x ≤ 3  π;
f[x_] := 
        0 /; (x > 3  π || x < 2  π);
r[t_] := 0 /; t < 1;
r[t_] := (ρ*c*f[c*t])/(2*ρ*c + τ) /; 
          t ≥ 1;
u1[x_] := 
      If[(0 ≤ x && x - t ≥ 0), 
        1/2 (f[x + c*t] + f[x - c*t]), 0]
u2[x_] := 
        If[(0 ≤ x && x - t ≤ 0), 
          1/2 (f[x + c*t] - f[-x + c*t]) + r[t - x/c], 
          0];
u3[x_] := 
      If[(0 ≥ x && x + t ≥ 0), r[t + x], 
        0]
g[x_] := 
        Plot[u1[x] + u2[x] + u3[x], {x, -15, 15}, 
          PlotRange -> {{0, 15}, {-1.1, 1.1}}, 
          DisplayFunction -> Identity];
D1[t_] := 
      Show[Graphics[{RGBColor[0, 0, 1], Thickness[0.007], 
            Line[{{0. , -4.9}, {0. , r[t]}}]}], 
        DisplayFunction -> Identity]
D2[t_] := 
      Show[Graphics[{RGBColor[0, 1, 1], 
            Polygon[{{-0.4, -3.0 + r[t]}, {0.4, -3.0 + 
                    r[t]}, {0.4, -4.7}, {-0.4, -4.7}}]}], 
        DisplayFunction -> Identity]
D3[t_] := 
      Show[Graphics[{RGBColor[0, 0, 1], Thickness[0.015], 
            Line[{{-0.4, -3.0 + r[t]}, {0.4, -3.0 + r[t]}}]}], 
        DisplayFunction -> Identity]
D4 = 
      Show[Graphics[{RGBColor[0, 0, 1], Thickness[0.007], 
            Line[{{-0.4, -1.5}, {-0.4, -4.7}}]}], 
        DisplayFunction -> Identity]
D5 = 
      Show[Graphics[{RGBColor[0, 0, 1], Thickness[0.007], 
            Line[{{-0.4, -4.7}, {0.4, -4.7}}]}], 
        DisplayFunction -> Identity]
D6 := 
      Show[Graphics[{RGBColor[0, 0, 1], Thickness[0.007], 
            Line[{{0.4, -4.7}, {0.4, -1.5}}]}], 
        DisplayFunction -> 
          Identity]

Table[
      Show[g[x], D1[t], D2[t], D3[t], D4, D5, D6, 
        PlotRange -> {{-15, 15}, {-6, 6}}, 
        DisplayFunction -> $DisplayFunction], {t, 0, 
        20,  .5}]