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?

The wave function for a travelling wave on a taut string is `y(x,t)=(0

1.	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?
Answer» `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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