How to derive equation for a transverse wave?

Question

I am trying to find an equation for the time it takes for a transverse wave to travel from one end to the other of a string with two fixed points.

The known values are Tension (T), mass of string (m), lenghth of string (L), and wave speed (v).

thanks for the help anyone

to the second answer- thanks, but that was the equation I used to find v , therefore there is no unknown variable in that equation.

Answer 1

v = sqrt(T/(m/L)). See the ref.

Answer 2

♣ ρ =m/L, v^2=T/ρ;
ρ* ∂[∂y/∂t]/∂t = T* ∂[∂y/∂x]/∂x; or;
∂[∂y/∂x]/∂x – (1/v^2) *∂[∂y/∂t]/∂t;

should i really derive this?