Harmonic waves

y(x,t) = Asin(kx - ωt + φ)

This is a wave traveling into the positive x-direction.

 k = 2π/λ, and ω = 2π/T = 2πf

v = λf = λ/T =  2πλ/(2πT) = ω/k

Let φ = 0.

Rewrite:

y(x,t) = Asin(kx - ωt)= Asin(k(x - (ω/k)t)) = Asin(k(x - vt))