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

Answer

A

Explanation

Take `y = A sin (omega t - kx)`
so `V_(p) = (del y)/(del t)`
`=- A cos omega cos(omega t - kx)`
`rArr V_(P)=omegasqrt(A^(2)-y^(2))=((2piv)/(lamda))sqrt(A^(2)-y^(2))`
`=(2pi(10xx10^(-2)))/(0.5)(sqrt((10)^(2)-(5)^(2)))xx10^(-2)`
`=(sqrt(3)pi)/(50)ms^(-1)`