How Do You Calculate Guitar String Length and Fret Placement Based on Frequency?

[Beasticly]

Homework Statement

Work out the length of a guitar string, and where the frets will be placed from nut to bridge given the starting frequency.

Frequency = 82.4Hz (E)

Homework Equations

12√2 between each fret

v = fλ

v = √(T/u)

u = m/L

L = (1/2)*λ

The Attempt at a Solution

I'm actually not too sure how to go about this question because I only have the frequency.

I guess I could approximate a tension and density by research but other than that I'm quite stumped.

Thanks in advance.

 

[mjsd]

how many frets in total do you want, it is 12?