The six strings of a guitar are tuned to the notes e (lowest frequency), a, d, g, b and e (highest frequency) with a range of two octaves between the two e strings. all the strings should be held under the same tension to avoid distortion of the neck of the guitar.

(a) if the high-frequency e string has a diameter of 0.30 mm, what should be the diameter of the low-frequency e string, assuming that both strings are made from the same material?
(b) the fundamental frequency of the high-frequency e string is 330 hz. if the distance between the nut and bridge of the guitar, i. e. the two fixed ends, is 65 cm and the strings are made of steel with a density of 7.7 x 103 kg m, find the total force acting on the neck of the guitar.
(c) if the high-frequency e string is made of nylon instead of steel what should be its diameter, assuming that the same tension is applied to it? (take the density of steel to be six times the density of nylon.)