It takes the sun(moon) 24h(24.8412h) to reach the same meridian (North-South), => f=((2π)/T)=(360/h)=>(OverTilde[D])=15(14.4)(Deg/h)
And look at what this seemingly tiny offset produces in sea-level:
η(t)=sin(2(Subscript[(OverTilde[D]), sol])t)+sin(2(Subscript[(OverTilde[D]), lun])t)

Import["/home/kirscher/Documents/vault/Vorlesungen/FIC_102/sidereal_day.png"]

iSize={700,500};
Manipulate[Grid[{{Plot[{Sin[k1 (x+(f1/k1)t)],Sin[k2 (x+(f2/k2)t)]},{x,-2 π,2 π},PlotRange->{-1.1,1.1},ImageSize->iSize,AspectRatio->2/5],Plot[{Sin[2 f1 t]+Sin[2 (f2) t],2 Cos[(f1-f2) t]},{t,0,31},PlotRange->{-2.5,2.5},ImageSize->iSize,AspectRatio->2/5,AxesLabel->{Style["time",FontSize->24],Style["water level",FontSize->24]},PlotLabel->Style[Framed["Interference of lunar and solar passage effects through\n a meridian ((Subscript[(OverTilde[D]), lun])≈14.4 Deg·(h^(-1)) and \!(Subscript[(OverTilde[D]), sun])≈15 Deg·(h^(-1)))"],20,Background->Lighter[Gray, 0.9],FontFamily->"Times"]]}}],"X1"->{{k1,1,"wave number 1"},1,10},"X2"->{{k2,1,"wave number 2"},1,100},"X3"->{{f1,1,"frequency 1"},15,15},"X4"->{{f2,1,"frequency 2"},14.4,14.9},"Y1Cyclic"->{{t,1,"time"},0,30}]

Now, let us do 2 dimensions ...

Hyperlink["Wave Interference","https://phet.colorado.edu/sims/html/wave-interference/latest/wave-interference_all.html"]

Manipulate[
 k = 2 π/λ;
 (*Dependence of the Intensity *)
 
 Show[If[graph1, {fig1[θ, a, d, k], fig2[d, λ, graph2],
     fig3[a, d, k], fig4[a, d, k]}, {fig1[θ, a, d, k], 
    fig2[d, λ, graph2], fig3[a, d, k]}], 
  PlotRange -> {{-60, 60}, {-80, 0}}, Frame -> None, 
  AspectRatio -> 3/5, ImageSize -> 1500],
 Grid[{{
    Item[Control[{{θ, 3.14/3, "θ"}, 3 3.14/4, 3.14/4, 
       0.02, ImageSize -> Large, Appearance -> "Labeled"}]
     , Alignment -> Right],
    Item[Control[{{λ, 8, "λ"}, 8, 12, 1, 
       ImageSize -> Large, Appearance -> "Labeled"}]
     , Alignment -> Right]},
   {Item[Control[{{a, 6, "A"}, 2, 10, .01, ImageSize -> Large, 
       Appearance -> "Labeled"}]
     , Alignment -> Right],
    Item[Control[{{d, 15, "d"}, 10, 20, ImageSize -> Large, 
       Appearance -> "Labeled"}]
     , Alignment -> Right]},
   {Item[Control[{{graph1, True, "graph"}, {True, False}}]], 
    Item[Control[{{graph2, True, "circle"}, {True, False}}]]}}, 
  Spacings -> {4, 0}],
 ControlPlacement -> Top, TrackedSymbols -> True, 
 SaveDefinitions -> True]

λ=2;
ampl=1;
nbrW=135;
vel=0.2;
Wav[x_,t_,n_]:=(ampl/n) (Sin[((2 π n)/λ) (vel t-x)]);
Animate[
Plot[Total[Table[Wav[rr,tt,nn],{nn,Range[1,nbrW,1]}]],{rr,-5,5},ImageSize->Large]
,{tt,0,20},AnimationRunning->False]

λ=8;
ampl=2;
nbrW=28;
vel=0.2;
Wav[x_,t_,n_]:=(ampl/n) (Sin[n ((2 π)/λ) (vel t-x)]);
Animate[
Plot[Total[Table[Wav[rr,tt,nn],{nn,Range[1,nbrW,2]}]],{rr,-5,5},ImageSize->Large]
,{tt,0,20},AnimationRunning->False]