OSCILLATIONS

Please provide a detailed solution

A transverse harmonic wave moves towards the right (positive sense) in the X direction has a amplitude of 4 cm, a wavelength of 4 cm and a frequency of 8 Hz. Determine: a) The speed of propagation of the wave. b) The initial phase if at x = 0 and t = 0 the elongation is - 2 cm. c) The mathematical expression of the wave. d) The distance separating two points on the X axis that oscillate with a phase difference of n/3 rad. Solution: a) 32 cm/s; b) 2n/3 rad; c) y (x, t) = 4 cos (17/2 x - 16n t - 2m/3) m; d) 2/3 cm