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

5

Explanation

`A_(eq) = sqrt(A_(1)^(2) + A_(2)^(2) + 2A_(1)A_(2) cos phi)`
`A_(eq) = sqrt(4^(2) + 3^(2) + 2(4)(3)cos"(pi)/(2))`
`A_(eq) = 5`.