Solid State Physics, 
Eric Toberer
Colorado School of Mines
Plane Waves

1-D Waves

The following considers a plane wave of form: A (e^(i(kx - wt)))

ClearAll["Global`*"]

Manipulate[Plot[
Re[A*Exp[I(k*x-ω*t)]],
{x,0,10},
PlotRange->2,AxesLabel->{"x","Real Amplitude"},PlotLabel->Style["Traveling Wave in 1D","Large"],ImageSize->Medium,BaseStyle->{FontSize->14}],{A,0.5,2,Appearance->"Labeled"},{k,-5,5,Appearance->"Labeled"},{ω,-5,5,Appearance->"Labeled"},{t,0,10,Appearance->"Labeled"}]

2 - D Waves

Now, we have a top-down view of 2-D plane wave. You can rotate the 3D box by clicking on it.  
In 2-D, (Overscript[k,  _]) is a vector.  So, we can now manipulate the angle θ of (OverBar[k]) as well as it’s magnitude.  I’ve coded it this way rather than building (OverBar[k]) out of k1 and k2 components. Either would work.

Manipulate[
Grid[{
{
Plot3D[Re[Exp[I(magk*Cos[θ]*x+magk*Sin[θ]*y-ω*t)]],{x,0,10},{y,0,10},PlotRange->1,AxesLabel->{"x","y","z"},PerformanceGoal->{"Quality"},ViewPoint->Top,ImageSize->Medium,Axes->{True,True,False},PlotLabel->"Traveling wave",BaseStyle->{FontSize->15}]
,
Graphics[{Red,Thick,Arrow[{{0,0},{magk*Cos[θ],magk*Sin[θ]}}]},Axes->True,PlotLabel->"k vector",PlotRange->{{-2,2},{-2,2}},ImageSize->Medium,BaseStyle->{FontSize->15}]}
}]
,{θ,0,2*π,Appearance->{"Labeled"}},{magk,1,3,Appearance->"Labeled"},{ω,0,1,Appearance->"Labeled"},{t,0,10,Appearance->"Labeled"}]