A transverse sinusoidal wave moves along a string in the positive x-direction at a speed of `10cm//s`. The wavelength of the wave is 0.5 m and its amplitude is `10 cm`. At a particular time t,the snapshot of the wave is shown in figure. The velocity of point P when its displacement is 5 cm is

(a) `sqrt(3pi)/(50)hatjm//s`
(b)`-sqrt(3pi)/(50)hatjm//s`
(c)`sqrt(3pi)/(50)hatim//s`
(d) `-sqrt(3pi)/(50)hatim//s`

Explanation

Particle velocity `v_p =-v` (slope of y-x graph)
Here, `v+=ve`,as the wave is travelling in positive x-direction. Slope at P is negative.
`:.` Velocity of particle is in positive `y`(or `hatj`) direction.
`:.` Correct option is (a).