Initialization

SetOptions[Plot,PlotStyle->{Red,AbsoluteThickness[2]},
ImageSize->800,AxesStyle->Directive[FontFamily->"Arial",FontSize->18,Black,AbsoluteThickness[0.5],Arrowheads[0.04]]];

Work

BASIC CONCEPTS IN WAVES : Displacement and force (or pressure) waves 

1 - D Waves, Oregon State University, Department of Physics. Janet Tate, 1997 - 2012

If the displacement of a particle, or a piece of rope or something else is represented by a sinusoidal wave, then the (-ve) derivative of that function is also a sinusoidal wave.  They each have a reflection and transmission coefficient (different from each other, but related to each other).  This sheet illustrates the concept of the displacement and pressure wave.

Watch the dots, centered on the ticks on the horizontal axis.  The red line plots the dispalcement; the blue the pressure.  Change colours to white to illustrate separately.

ψ[x_,t_]:=1*Cos[k*x-ω*t]

ψ[x_,t_]:=1*Sin[k*x]*Cos[ω*t]

ω=2*π;
k=2*π;

int=0.125;amp=.03;
Animate[Plot[{ψ[x,t],-(1/ω)*Derivative[1,0][ψ][x,t]},{x,-1,1},
PlotStyle->{{Red,AbsoluteThickness[3]},{Blue,AbsoluteThickness[3]}},
AxesLabel->{x,"Disp,Pressure"},
PlotLabel-> Style["t = "<>ToString[t],16,FontFamily->"Arial"],
Ticks-> {Table[{int*i,"",0.1},{i,-10,10}],None},
Epilog->{Gray,PointSize[0.02],Point[Table[{x+amp*ψ[x,t],0},{x,-1,1,int}]]}],
{t,0,2},
AnimationRate->0.2,
AnimationRunning->False]

Animate[Graphics[Point[Table[{x+amp*ψ[x,t],0},{x,-2,2,0.125}]],ImageSize->800],{t,0,2},AnimationRate->0.5,AnimationRunning->False]