No idea how to do the second part, please help. A violin string has a length of

Question

No idea how to do the second part, please help.

A violin string has a length of 0.310 m and is tuned to concert G, with f_g=392 Hz. How far from the end of the string must the violinist place her finger to play concert A, with = 440 Hz? If this position is to remain correct to one-half the width of a finger (that is, to within 0.540 cm), what is the maximum allowable percentage change in the string tension? Your response differs from the correct answer by more than 10%. Double check your calculations.%

Explanation / Answer

"If this position is to remain correct to one-half the width of a finger" etc. - I understand this part of question as if allowed tolerance for L2 is ±0.54cm = ± 0.0054m
That would correspond to allowed relative change of length (let's denote it by ) is:
= L / L2 = ±0.0054/0.276 = ± 0.01957= ± 1.957%
because length is inversely proportional to square root of tension we can write
1+ = 1/(1+T)
where is maximum allowable relative change of tension.
square both sides:
(1+)² = 1/(1+T)
T = 1/(1+)² - 1
T= 1/(1± 0.01957)² - 1 = 0.038 = 3.8%

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