How Does Doubling the Radius of a String Affect Its Wave Speed?

[aa1515]

Homework Statement

A wave travels along a string at a speed of 261 m/s. What will be the speed if the string is replaced by one made of the same material and under the same tension but having twice the radius?

Homework Equations

v=squareroot(T/mu) (where T=tension)

mu=m/L (where m= mass and L= length)

The Attempt at a Solution

I'm not sure how I need to manipulate mu to accomadate for twice the radius. Volume would change, but wouldn't mass as well? I thought maybe I would need to use density, but we are not given the density of the string. Do I assume the mass doesn't change because the tension is the same? Fatter strings are supposed to go slower. So I'm really stuck on what to do..Help please?!

 

[Redbelly98]

Doubling the radius will change the linear density by a certain factor, which you'll need to figure out. I.e., if the radius is twice as big, then the volume (and hence mass) of a 1 m long string will be larger by what factor?