k being the one from the harmonic wave ψ(x,t) = Asin(kx - ωt) where k = 2π/λ The way I see it right now, k is just defined this way to get the period of sin(x) to be λ by using sin(kx), so I wondered if there's something more to it. (Though I know it can be used as an vector to declare the direction of the wave.) I played with the trig stuff a bit. I know that a harmonic wave can be traced by a point in a circular motion. sin(x) traces the circle with a period of 2π so I take that to be a circle with 2π circumference and radius 1. Doing the same with sin(kx) gets a circle with λ circumference and radius 1/k. So k seems to be related to 1/r or the curvature? I found it interesting too that if I directly substitute k with 1/r, the ω in ω = v/r from mechanics can be found with the ω in ω = kv from waves. Is there some insight to take away from this?