A child playing with a long rope ties one end 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 `3` Hz.
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 quetions.
(Also assume that the wave propagates along the positive `x-`direction.)
A wave function that describe the wave in the given sutuation is

Options

A. `y=-(0.1 m) cos(12.5 rad//s)t
B. `y=0.1 mcos (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

Explanation

`omega=2pif=6pi rad//s`
and `k=(omega)/(v)=(6pi)/(15)=1.26`
`y=0.1 cos(1.26x-18.8t)`
At point `2.5 m` from child and equation of displacement time to reach `2.5 m`=T//2`
`Deltaphi=(2piDeltat)/(T)=pi`