How the wave equation relates to Newton's Second Law of Motion

[Rich667]

Homework Statement

Open Question 3.bmp

Homework Equations

The Attempt at a Solution

Open Answer 3.bmp

Any help with this would be greatly appreciated

 

[JohnSimpson]

consider a small sting segment with (different) tension force vectors acting on each end, and write down Newtons second law in two orthogonal directions

 

[yudong_cao]

I think the problem lies in the definition of F and acceleration a. In answer 3.bmp the F is defined as the tension in the rope, which is coaxial to the string, while the second derivative of y , the acceleration of an element with coordinate (x,y), is vertical to the string. Surely you can't say F=ma with F and a pointing to 2 different directions.