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`

Options

A. `(sqrt(3 pi))/(50) hat j m//s`
B. `-(sqrt(3 pi))/(50) hat j m//s`
C. `(sqrt(3 pi))/(50) hat i m//s`
D. `-(sqrt(3 pi))/(50) hat i m//s`

Answer

A

Explanation

Particle velocity, `vp = -v` (slope of y - x graph)
Here, `v = + ve`, as the wave is travelling in positive direction.
Slope at `P` is negative.
Therefore, velocity of particle is in negative `y` (or `hat j`) direction.