f = Sin[x]/x

Plot[f, {x, -40, 40}, PlotRange -> {- .5, 1}]

\(\(\(
\)\(fp = Sin[x + v\ t]/\((x + v\ t)\)\)\)\)

\(\(\(
\)\(fm = Sin[x - v\ t]/\((x - v\ t)\)\)\)\)

v = 2

\(\(\(
\)\(Do[
      Plot[{fp}, {x, \(-40\), 40}, PlotRange -> {\(- .5\), 1}], {t, 0, 20, 
        2}]\)\)\)

Do[Plot[fp, {t, -40, 40}, PlotRange -> {- .5, 1}], {x, 0, 20, 
        2}]

Do[Plot[{fm}, {x, -40, 40}, PlotRange -> {- .5, 1}], {t, 0, 20, 
        2}]

Do[Plot[{fm + fp}, {x, -40, 40}, PlotRange -> {- .5, 2}], {t, 
        0, 20, 2}]

gm = Sin[x - v t]

gp = Sin[x + v t]

Do[Plot[gm, {x, -10, 10}, PlotRange -> {-1, 1}], {t, 0, 
        20, 2}]