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First of all, can I clear up that this refers to transverse velocity yes, and not phase velocity??? (My book isn't clear).These are all partial derivatives by the way, so i presume it's all to do with transverse velocity and not phase since we keep x constant???

I can't really right the entire equation out, so I'll do my best.

So, I end up with an equation with (d^2y/dx^2) = (F/(mu)) (d^2y/dt^2)

and then you compare this to the wave equation.

I don't understand where the left side comes from. The limit as the length goes to 0 is taken of the net force acting on the string. But how do we end up with the second derivative (curvature of string) of y/x when we do this??? What is the logic behind it?

Thank you guys!!!

Sorry for any mistakes, I don't have my book handy.