[UPSC CSE 2001] Waves (Q63, 20M)

Certain string has a linear mass density of 0.25\text{ kgm}^{-1} and stretched with a tension of 25 N. One end is given a sinusoidal motion, its frequency 5 Hz and amplitude 0.01 metre. If at t = 0, the end has zero displacement and is moving along the positive Y direction, derive the wave speed, the wavelength and the wave equation of the wave in the string.