Figure given shows a sinusoidal wave on a string. If the frequency of the wave is 150 Hz, what is the velocity and wavelength of the given wave?

Answer

(a) `10 pi rad//s` , (b) `pi//2 pi rad//s` , (c) `y = (12 xx 10^(-2)m) sin ((pi)/(2)x - 10 pit)` , (d) `(6)/(5) pi m//s` (e) `12 pi^(2) m//s^(2)`

Explanation

(a) `omega = 2pif = 10 pi` Red/sec
`(b) lambda xx 5 = 20 , lambda = 4 m , K = (2pi)/(lambda) = (pi)/(2) rad//m`
(c) ` y = 12 xx 10^(-2) sin (omegat - kx + phi) = 12 xx 10^(2) sin (10 pit - (pi)/(2) + phi)`
At `t = 0 , x = 0 , y = 0`
`(delx)/(delx) = 12 xx 10^(-2) (-(pi)/(2)) cos "(100 pit - (pi)/(2)x+phi)`
At `t = 0 , x = 0`
`(dely)/(delx) = -12 xx 10^(-2) ((pi)/(2)) cos phi`
`(dely)/(delx)` should be positive `:. phi = pi`
`y = 12 xx 10^(-2) sin (10 pit - (pi)/(2) + pi)= 12 xx 10^(-2) sin ((pi)/(2)xx-10 pit)`
At `t = 0 , x = 0`
`(dely)/(delx) = -12 xx 10^(-2) ((pi)/(2)) cos phi`
`(dely)/(delx)` should be positive
`y = 12 xx 10^(-2) sin (10pit - (pi)/(2)x + pi) = 12 xx 10^(-2) sin ((pi)/(2) x - 10 pit)`
(d) `V_(max) = Aomega = 12 xx 10^(-2) xx 10 pi xx 10 pi = 12pi^(2)`
(e) `A_("max") = Aomega^(2)`
`= 12 xx 10^(-2) xx 10pi xx 10pi = 12 pi^(2)`