Velocity of Wave in Twice the Radius String: V = root(Tension/mu) * root2

[lostie100]

A wave travels along a string at a speed of 280m/s. What will the speed if the string is replaced by one made of the same material and under the same tension but having twice the radius?

V = root (Tension/mu)

mu = mass/length

length is 2radii

I manipulated the formulas, however, apparently you divide the velocity by 2, but I found it to be multiplied by root2.
Please show me the manipulation of the formulas...

 

[LowlyPion]

Assuming uniform density what happens when you double the cross-section of the string that remains the same length? Does the total mass of the string change? By how much?

Plug in your numbers then and see what happens.

 

[lostie100]

The mass also doubles...but I don't see how it relates to the other formula for velocity...