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    Wavelength and frequency

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    As the drawing shows, the length of a guitar string is 0.628 m. The frets are numbered for convenience. A performer can play a musical scale on a single string, because the spacing between the frets is designed according to the following rule: When the string is pushed against any fret j, the fundamental frequency of the shortened string is larger by a factor of the twelfth root of two (122) than it is when the string is pushed against the fret j - 1.

    Assuming that the tension in the string is the same for any note, find the spacing
    (a) between fret 4 and fret 3
    1 cm and
    (b) between fret 9 and fret 8
    2 cm.

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    Solution Summary

    The solution shows how to derive the expression for the distances between consecutive frets of a guitar.