The speed of the wave is how fast the crest of the wave moves forward, not the up and down speed of the circles. Since velocity is the rate of change of position, the transverse velocity in the y ...The speed of the wave is how fast the crest of the wave moves forward, not the up and down speed of the circles. Since velocity is the rate of change of position, the transverse velocity in the y direction is given by the derivative of the displacement with respect to time: v(x,t)=∂y(x,t)/∂t=−Aωcos(kx−ωt+ϕ) where k=2π/λ is called the wave number and ω=2πf as before.
