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

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To calculate the length of a guitar string and fret placement based on a frequency of 82.4Hz, one must use the formula v = fλ, where v is the wave speed, and λ is the wavelength. The tension (T) and linear density (u) of the string can be estimated through research to find the wave speed. The fret placement can be determined using the formula for the length of the string, L = (1/2)λ, and the 12th root of 2 for spacing between frets. The total number of frets typically considered is 12. Understanding these calculations will help accurately position the frets for the desired frequency.
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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.
 
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how many frets in total do you want, it is 12?
 

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