Fundamental frequency and tension

[k77i]

Homework Statement

A guitar string has a fundamental frequency of 429 Hz when its tension is 259 N.
The string is being tuned to a fundamental frequency of 388 Hz. What is the required tension?

Homework Equations

v = sqrt(T/u): where v is the speed, T is the tension and u is the linear mass density
f1 = v/2L: where f1 is the fundamental frequency, v is the speed again and L the length of the string

The Attempt at a Solution

sqrt(T/u) = f1(2L)
sqrt(259/u) = 858L

I tried to use the speed equations to find u or L, which would allow me to calculate the v after and then get the frequency, but I'm still left with 2 unknowns. Am I using the wrong equations to solve this?

 

[Stonebridge]

You have two equations, one for f1=429Hz and one for f2=259Hz
Write each one as f=v/2L and substitute for v in terms of T and u
Then do f2/f1=

 

[k77i]

Oh I get it now. It should have been obvious but I was just having trouble with cancelling out the unknown terms. Thanks I managed to get the answer.