using a wave function plotter, i happen to know for transverse traveling wave the formula is



[b][color=blue]transverse wave

U(x,t) = U[sub]o[/sub]*sin(w*x-t)                        for right traveling wave[/color]

[color=red]for stationary wave

U(x,t) = sin(t)*U[sub]o[/sub]*sin(w*x)
or
U(x,t) = U[sub]o[/sub]*sin(w*x-t)  +U[sub]o[/sub]*sin(w*x+t)  [/color]

[color=brown]for longitudinal wave

each particle is doing a motion U(x,t) = U[sub]o[/sub]*sin(w*x-t)  about it's own equlibrium with each obeying U[sub]o[/sub]*sin(w*x-t)

i did by  _view.trail.addPoint(x+0.9*u,0);

if you line them it will appear to be a longitudinal traveling wave[/color]


[color=teal]for stationary longitudinal wave
i suspect adding
U(x,t) = U[sub]o[/sub]*sin(w*x-t)  +U[sub]o[/sub]*sin(w*x+t) 
will work.[/color][/b]

but i am not sure if it is pressure, will the equation need to differentiate? testing now


i await Prof hwang to reply