A child, playing with a long rope, ties one end and holds the other. The rope is stretched taut along the horizontal. The child shakes the end he is holding, up and down, in a sinusoidal manner with amplitude 10 cm and frequency 3Hz. Speed of the wave is 15 m/s and, at t=0, displacement at the child's end is maximum positive. Assuming that there is no wave reflected from the fixed end, so that the waves in the rope are plane progressive waves, answer the following questions (also assume that the wave propagates along the positive x-direction)
Equation of displacement of a point 2.5m from the child's cnd can be expressed as

Options

A. y = -(0.1 m) cos (18.8 rad / s) t
B. y = (0.1 m) cos (12.5 rad / s) t
C. y = (0.1 m) sin (4 rad / s) t
D. y = -(0.1 m) sin (10 rad / s) t

Answer

A