A wave on a string is described by its wavefunction y(x,t) = 0.014 sin (5x + 30t - π/3). Determine the magnitude of the transverse velocity of an element of the string with a vertical displacement y(x,t) = 0.
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 = -Aω cos (k x - ω t + φ) where k = 2π/λ is called the wave number and ω = 2πf
so, what do you get?