f[x_]  :=  Sin[x];

p =. ; q =. ;

p[t_, x_]  :=  ((f[x  -  t] )/2); 
    q[t_, x_]  :=  f[x  +  t]/2; 
    u[t_, x_]  :=  p[t, x] + q[t, x];

\(\(\(\ \)\(\(δt\  = \  .05\)\(;\)\(\ \)\(\(Plot[{p[#, x], 
            q[#, x], u[#, x]}, {x, \(-5\), 5}, 
          PlotRange\  -> {\(-1.2\), 1.2}, 
          PlotStyle\  -> {\ {Thickness[ .004], 
                Hue[ .05]}, \ {Thickness[ .004], 
                Hue[ .45]}, \ {Thickness[ .004], 
                Hue[ .75]}}] &\)\  /@ 
\((	\ Range[0, 
          2  π, δt])\)\)\(;\)\(
\)\(
\)\)\)\)