How Do You Calculate the Period of a Traveling Wave?

[Noctix]

Homework Statement

At x = 15.0 cm and t = 2.00 s, the displacement of a traveling wave is 8.66 cm. The amplitude of the wave is 10.0 cm, and its wavelength is 8.00 cm. Assume the smallest positive phase angle.
What is its period?

Homework Equations

y(x,t)=y₀sin2pi(x/lambda-t/period)

The Attempt at a Solution

y(2)=10sin(8.66/8-2/T)

I don't know if I set it up right, and I don't knw how to solve the equation from here because i don't know the value of y... any and all help is greatly appreciated.

 

[HallsofIvy]

The period of the wave is the same no matter what t is so take t to be a fixed number, 0 is simplest. Then we have y(x)= y_0 sin(2\pi (x/\lambda).

We know that the period of "sin(x)" alone is 2\pi- so that one period of sin(2\pi(x/\lambda)) will occur between 2\pi(x/\lambda)= 0 and 2\pi(x/\lambda)= 2\pi.

 

[Noctix]

The period of the wave is the same no matter what t is so take t to be a fixed number, 0 is simplest. Then we have y(x)= y_0 sin(2\pi (x/\lambda).

We know that the period of "sin(x)" alone is 2\pi- so that one period of sin(2\pi(x/\lambda)) will occur between 2\pi(x/\lambda)= 0 and 2\pi(x/\lambda)= 2\pi.

sorry, i don't quite understand what you're saying. If we use t=0, the period is canceled out of the equation, isn't it? even if not, how do i get an answer out of your two final equations?
sorry for being slow... i haven't had trig, so this is all really new to me.
also, I should have mentioned this earlier, but I'm aiming for the answer period=1.17s