Review Conceptual Example 5 before attempting this problem. Asthe drawing shows,

Question

Review Conceptual Example 5 before attempting this problem. Asthe drawing shows, the length of a guitar string is 0.599 m. Thefrets are numbered for convenience. A performer can play a musicalscale on a single string because the spacing between thefrets is designed according to the following rule: When thestring is pushed against any fret j, the fundamentalfrequency of the shortened string is larger by a factor of thetwelfth root of two than it is when the string is pushed againstthe fret j - 1. Assuming that the tension in the string isthe same for any note, find the spacing (a)between fret 1 and fret 0 and (b) between fret 7and fret 6. For a, I got 2.95, and for b, I got a value of 0.63, but theseare invalid

Explanation / Answer

    in the given problem we can see that thelength of the unfretted string is
    Lo = v / 2 fo
    the frequencies corresponding to the first andzeroth frets are
    L0 - L1 = (v / 2f0) - (v / 2 f1)
               = (v / 2 fo) [(1 -(fo / f1)]
               = (v / 2 fo) [1 - (1 /(122]
               = Lo [1 - (1 / 122)]
               = ......... m
    in the similar manner solve for 7 and 6

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