Function for y(x,t) wave some questions

[yjk91]

Homework Statement

A wave travels along a string in the positive x-direction at 33 m/s. The frequency of the wave is 48 Hz. At x = 0 and t = 0, the wave velocity is 2.8 m/s and the vertical displacement is y = 3 mm. Write the function y(x, t) for the wave. (Use the following as necessary: x and t. Assume x and y are in m, and that t is in s.)

The Attempt at a Solution

y(x,t) = Acos(kx - wt)
should be the formula

i'm assuming A = 0.003m but it is not so i don't know

w = 2 * pi * f (frequency)
= 2 * pi * 48Hz
= 301.59

k = w / v
= 301.59 / 33(m/s)
= 9.139

so what i have now is y(x,t) = Acos(9.139x - 301.59t + something)

how do i find the amplitude and the missing something if there is one?

thank you

 

[Liquidxlax]

your vertical displacement y(x,t) would be 3mm since at t=0 and x=0 , y=3mm

y(x,t) = Acos( k(0) - w(0)) = A(1) = 3mm = 0.003m

what you have looks right to me. Sorry if its not to clear, it's been a long summer

 

[yjk91]

your vertical displacement y(x,t) would be 3mm since at t=0 and x=0 , y=3mm

y(x,t) = Acos( k(0) - w(0)) = A(1) = 3mm = 0.003m

what you have looks right to me. Sorry if its not to clear, it's been a long summer

one example was this question

A wave travels along a string in the positive x-direction at 31 m/s. The frequency of the wave is 47 Hz. At x = 0 and t = 0, the wave velocity is 2.8 m/s and the vertical displacement is y = 3 mm. Write the function y(x, t) for the wave. (Use the following as necessary: x and t. Assume x and y are in m, and that t is in s.)

the answer was 0.0099 * sin(9.53*x - 295.31*t + 2.84)

i know how to get the k and w which was 9.53 and 295.31
but i don't know how to get 0.0099 and 295.31 are
thank you

i know how to get the k and w which are 9.

 

[ehild]

Find the velocity of the piece of string at x=0, t=0, by taking the time derivative of your function. Then there two equations for the unknown amplitude A and phase constant (something)

ehild