Can string diameter affect wave speed in guitar strings?

[map7s]

Two steel guitar strings have the same length. String A has a diameter of 0.50 mm and is under 340.0 N of tension. String B has a diameter of 1.0 mm and is under a tension of 800.0 N. Find the ratio of the wave speeds, vA / vB, in these two strings.

I know that the equation that I need to use is v=square root of F/u where u=the mass per length of the string. I tried doing this solving by using that equation and just plugging in the diameters. Now that I've actually sat down and thought about it, I was wondering how I could incorporate the diameters into that equation, namely how can I figure out how to the diameter is related to the mass per length ?

 

[OlderDan]

The problem is assuming the strings are made of the same material, so they have the same mass per unit volume. A string with greater diameter has more volume, and hence more mass for a given length than a string with smaller diameter. Figure out the ratio of mass per unit length of the two strings by figuring out the ratio of the volumes of equal lengths of the strings

 

[map7s]

So the volume would be 2pi*r^2*h but h would be the same for both equations and the 2pi would be constant and therefore cancel out when plugged into a ratio. So the overall equation would be something like v ratio=[square root of F/(r^2)] / same thing with the next set of numbers...right ?

 

[OlderDan]

So the volume would be 2pi*r^2*h but h would be the same for both equations and the 2pi would be constant and therefore cancel out when plugged into a ratio. So the overall equation would be something like v ratio=[square root of F/(r^2)] / same thing with the next set of numbers...right ?

That's the right idea. Don't lose track of the constants, though they will divide out if you do a ratio.