Help Needed: Solving y = A sin({2*10^6 ({\pi / 3 -\pi t }) + \phi })

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The discussion revolves around solving the equation y = A sin(2*10^6 (π/3 - πt) + φ) and determining the time variable t. The formula for signal strength s(x, t) is mentioned, but the focus is on finding the time for the signal to travel a distance of 1.0 x 10^6 m. To calculate this time, the speed of the wave (v) must be determined from the given data. The key question is whether the speed can be derived from the provided information.
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Homework Statement
Exercise
Relevant Equations
##v = f \lambda , s({x,t}) = A sin({k x - \omega t + \phi}) ##, other statements are provided in the picture.
I know so ## y = A sin({2*10^6 ({\pi / 3 -\pi t }) + \phi }) ##
There still some unknown I cannot find, can anyone give me some hint please?
 

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But how can I find t?## \lambda = 3 ## because ## k = 2 \pi/3 = 2 \pi/\lambda##
 
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MichaelTam said:
But how can I find t?## \lambda = 3 ## because ## k = 2 \pi/3 = 2 \pi/\lambda##
The formula ##s(x, t) = A sin(k \cdot x - \omega \cdot t + \phi)## gives you the signal strength (##s##) at a particular position (##x##) and time (##t##). If you wanted the time at which ##s## had some particular value, you would use the formula. But that is not what the question is about.

You simply want the time for the signal to travel a distance of ##1.0 \times10^6 ## m. So you use:

##time = \frac {distance}{speed}##

You know the distance is ##1.0 \times 10^6 ## m. So the real question is can you find the speed (##v##) of the wave from the data supplied?

Edit: minor changes to improve wording.
 
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