String hanging from the ceiling

[rbwang1225]

Homework Statement

A string of length L and mass m, hanging an object of mass M from the ceiling. After sending a transverse pulse from the top of the string , how much time we have to wait until the reflected pulse returned to the top?

Homework Equations

The time interval for a transverse pulse to travel the legth of the rope is $Δt=2\sqrt{\frac{L}{mg}}(\sqrt{M+m}-\sqrt M)$.

The Attempt at a Solution

I think the time for waiting is just twice of Δt, but I still concern that maybe I miss something.

Sincerely.

 

[voko]

Where does that equation come from?

 

[rbwang1225]

It is from that different points on the string have posses different wave speeds.