Wave on a string tied to a weight

[Issacros]

Homework Statement

A 17 m string of weight 13kg is tied to the ceiling at its upper end, and the lower is tied to a weight of 13 kg. how long will it take a wave to get from one end to the next? (g=10 m/s^2)

Homework Equations

v = (T/u)^(1/2)

The Attempt at a Solution

well, i think mass(y)=(13+13y/17)kg
therefor T=ma= (13+13y/17)kg*19m/(s^2)
V(y)=(T/u)^(1/2)=>> (10y)^1/2

beyond this point I'm stuck. Thanks in advance.

 

[Doc Al]

well, i think mass(y)=(13+13y/17)kg

OK, this is the total mass for all points below y (measured from the bottom of the string).

therefor T=ma= (13+13y/17)kg*19m/(s^2)

Where did you get 19 m/s^2? The tension at point y is equal to the weight of the mass below that point.

V(y)=(T/u)^(1/2)=>> (10y)^1/2

Not sure where this last expression came from. Use the correct expression for T(y).

Hint:
V(y) = (T/μ)^(1/2)
dy/dt = (T/μ)^(1/2)

Rearrange and integrate to find the total time.