f =  Cos[w1 t]  +  Cos[w2 t]

w1 = 1

w2 = 1.1

Plot[f, {t, -130, 130}]

wp = (w1 + w2)/2

wm = (w1 - w2)/2

g = 2 Cos[wm t] * Cos[wp t]

Plot[g, {t, -30, 30}]

p = 
      Integrate[(A Sin[w t] + B Cos[w t]) /. t -> 1, {w, 0, 30}]

A =  0

B =  1/(w4 - w3)

Plot[B Cos[w t] /. t -> 1, {w, w3, w4}]

r = Integrate[B Cos[w t], {w, w3, w4}]

w3 = 1

w4 = 10

Plot[r, {t, -20, 20}, PlotRange -> {-.6, 1.1}]

q = 
      Sin[(w4 - w3)*t/2]/((w4 - w3)*t/2) *
        Cos[(w3 + w4) t/2]

Plot[q, {t, -20, 20}, PlotRange -> {-.6, 1.1}]

\(\(
k = w/v\)\)

\(\(v = 10
\)\)

d = 1

\(\(
y = Integrate[B\ Cos[w\ x/v\  - w\ t] /. x -> 1, {w, w3, w4}]\)\)

\(
\)

Do[{psi = Integrate[B Cos[w x /v - w t] /. t -> n*d, {w, w3, w4}], 
        Plot[psi, {x, -200, 200}, PlotRange -> {-.5, 1}]}, {n, 1, 10}]

Do[{
        psi = Integrate[
            B Cos[w^2 x /(5  v) - w t] /. t -> n*d, {w, w3, w4}], 
        Plot[psi, {x, -200, 200}, PlotRange -> {-.5, 1}]}, {n, 0, 10}]

Do[{
        psi = Integrate[
            B Cos[w^2 x /(5  v) - w t] /. x -> n*d, {w, w3, w4}], 
        Plot[psi, {t, -20, 20}, PlotRange -> {-.5, 1}]}, {n, 0, 10}]