Wave equation in 3D — initial velocity in unit sphere

u[r_]  :=  
      Which[t < 1 - r , 
        t, (t > Abs[1 - r] ) &&  (t < 
              r + 1), ((1 - (((r - t))^2))/(4 r )), 
        True, 0]

Do[Plot[Evaluate[u[r]], {r, 0, 3},  
        PlotRange  ->  {{0, 3}, {- .1, 1.23}},  
        AspectRatio  ->   .6,  
        PlotStyle  ->  {Hue[ .6], Thickness[ .006]}], {t, 0, 
        4,  .05}]

Wave equation in 3D — initial displacement in unit sphere

u[r_]  :=  
      Which[t < 1 - r , 
        1, (t > Abs[1 - r] ) &&  (t < 
              r + 1), ((r - t)/(2 r )), True, 
        0]

Do[Plot[Evaluate[u[r]], {r, 0, 3},  
        PlotRange  ->  {{0, 3}, {-2.1, 1.1}},  AspectRatio  ->  1,  
        PlotStyle  ->  {Hue[ .95], Thickness[ .006]}], {t, 0, 
        4,  .05}]

Wave equation in 2D — fundamental solution

u[r_]  :=  
      Which[r < t , (1/(2  π (Sqrt[ (t^2)  -  (r^2)]))), True, 
        0]

Do[
        Plot[Evaluate[u[r]], {r, 0, 3},  
          PlotRange  ->  {{0, 3}, {- .1, 2}},  
          AspectRatio  ->   .6,  
          PlotStyle  ->   {Hue[ .35], Thickness[ .006]}], {t, 0, 
          4,  .05}];