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

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`.