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The wave funcation for a travelling wave...

The wave funcation for a travelling wave on a string in given as
`y (x, t) = (0.350 m) sin (10 pi t - 3pix + (pi)/(4))`
(a) What are the speed and direction of travel of the wave ?
(b) What is the vertical displacement of the string at `t = 0, x = 0.1 m` ?

Text Solution

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`Y(x,t) = (0.350m) sin (10pit - 3pi x + (pi)/(4))`
comparing with equation ,
`Y = A sin (omegat - kx + phi) , omega = 10 pi , k = 3pi, f = (pi)/(4)`
(a) speed `= (omega)/(k) = (10)/(3) = 3.33 m//sec` and along `+ve x` axis
(b) `y(0.1, 0) = 0.35 sin (10 pi xx O - 3 pi (0.1) + (pi)/(4)) = 0.35 sin [(pi)/(4) - (3pi)/(10)] = -5.48 cm`
(c) `k = (2pi)/(lambda) = 3 pi rArr lambda = (2)/(3) cm , = 0.67 cm` and `f = (v)/(lambda) = (10//3)/(2//3) = 5 Hz`.
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