The wave function for a travelling wave on a taut string is
`y(x,t)=(0.350 m)sin(10pit-3pix+pi//4)`. (SI units)
(a) what is the speed and direction of travel of the wave ?
(b) what if the verticaly position of an element of the string at `t=0, x=0.100 m?`
(c ) what is the wavelength and frequency of the wave?
(d) waht is the maximum transverse speed of an element of the string?

Explanation

`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`.