The physics
A wave shape that moves without changing is y = f(x − vt). It moves at v toward +x. With x + vt it moves toward −x.
y = f(x − vt) f(bx + ct): speed c/b
A shaker makes a sine wave. A is its biggest height. ω sets how fast it shakes. k sets how long each wave is.
y = A sin(ωt − kx) f = ω/2π λ = 2π/k v = fλ
Along the wave the phase changes by 360° over one wavelength. Each bead moves up and down in SHM. Its velocity is Aω cos(ωt − kx), and its top speed is Aω.
The wave carries energy down the string. The power grows as the square of the amplitude and of the frequency.
v = √(T/μ) P = ½ μ v ω² A²