What is the Time Required for a Transverse Wave to Travel in a Whirled Rope?

[pjkily]

Homework Statement

a uniform rope with length L and mass M is held at one end and whirled in a horizontal circle with angular velocity $$\omega$$. you can ignore the force of gravity on the rope. find the time required for a transverse wave to travel from one end of the rope to the other.

Homework Equations

v=(T/$$\mu$$)^(1/2) where $$\mu$$=density
$$\Sigma$$F=ma

The Attempt at a Solution

This is the solution that the professor gave, but i don't understand why:

$$\Sigma$$F=F$$_{T}$$=$$\Delta$$a$$_{c}$$
dF$$_{T}$$=(dm)r$$\omega$$$$^{2}$$
dF$$_{T}$$=$$\mu$$r$$\omega$$$$^{2}$$dr
integrate with respect to r, from r to t.

I

 

[tiny-tim]

Welcome to PF!

Hi pjkily! Welcome to PF!

(have a square-root: √ and a mu: µ and an omega: ω and a sigma: ∑ and a delta: ∆ )

a uniform rope with length L and mass M is held at one end and whirled in a horizontal circle with angular velocity $$\omega$$. you can ignore the force of gravity on the rope. find the time required for a transverse wave to travel from one end of the rope to the other.

The tension, T (no need to call it F_T ) increases towards the end of the string.

And the speed depends on the tension.

So you need to integrate along the string.

 

[pjkily]

OH! that's the part I didn't understand.
THANK YOU SOOOO MUCH, Tim!