A steel guitar string has linear mass density μ=6.4×10−3kgm−1 and can be stretched to a maximum safe tension of 90N. It is required to tune the string to produce a musical note of frequency 256Hz in its fundamental mode.
(i) Calculate the minimum length of the string that will allow it to be tuned to this note without exceeding the safe tension.
(ii) The same string is fixed at the length found in part (i). The performer wishes to raise the note to 288Hz by increasing the tension only. Determine the new tension needed.