A travelling wave on a string is given by `y = A sin [alphax + betat + (pi)/(6)]`. If `alpha = 0.56 //cm, beta = 12//sec, A = 7.5 cm`, then find the position and velocity of particle at `x = 1 cm` and `t = 1s` is

Options

A. `4.6 cm, 46.5 cm s^(-1)`
B. `3.75 cm, 77.94 cm s^(-1)`
C. `1.76 cm, 7.5 cm s^(-1)`
D. `7.5 cm, 75 cm s^(-1)`

Answer

B

Explanation

Put `alpha, beta, A, x` and `t` in the equation
`(2pi)/(lambda) = 0.56 cm^(-1)`
`2pif = 2 sec^(-1)`
`alphabeta + betat + (pi)/(6) = (12.56 xx 180)/(3.14) + 30 = 750^(@)`
`y = 7.5 cm sin 750^(@) = 3.75 cm`.
`v = (dy)/(dt) = Abetacos(alphax + betat + (pi)/(6)) = 7.5 xx 12 xx (sqrt(3))/(2) = 77.64 cm//sec`.