Prove that if a transverse sinusoidal wave is travelling along a string, then the slope at any point of the string is equal to the ratio of the particle speed to wave speed at that point.
The Attempt at a Solution
This is what i did isn't the equation for transverse = y=Asin(kx-wt)
So i differentiate it with respect to "t" therefore getting dy/dt = -wAcos(kx - wt)
cos(kx - wt) = 1
therefore dy/dt = -wA and w = 2pi(F)
So wouldn't it be equal to 2pi(F)A <------------------ just want to make sure but this is for the particle speed??
If so how am i to that the ratio of the particle speed to wave speed at that point is equal???