A nylon string of length 0.90m is kept under a tension of 81N. The string is found to produce a frequency of 675Hz when vibrating in its fifth harmonic.
(i) Determine the linear mass density of the string.
(ii) Calculate the frequency of the fundamental mode of the string under the same tension.
(iii) The same string is now used in another instrument where its fundamental frequency has to be 600Hz while the tension remains 81N. By pressing the string against a fret, the vibrating length is adjusted. Find the length of the vibrating portion required to obtain the desired fundamental frequency.