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**A rope of total mass M and length L is suspended vertically.Show that a transverse wave pulse travel in the length of the rope in a time t=2(L/g)^0.5**

If i take the distance of any point on the rope ,A, from the lower end to be X.

linear density is M/L

Tension due to the segment of rope below A is MgX/L

velocity =(T/linear mass density)^0.5

=(L^2/Xg)^0.5

if X=L

V= (L/g)^0.5

which is not what is needed to be shown. So where am i wrong?