As the drawing shows, the length of a guitar string is 0.599m. The frets are num

Question

As the drawing shows, the length of a guitar string is 0.599m. The frets are numbered for convenience. A performer can play amusical scale on a single string because the spacing betweenthe frets is designed according to the following rule: Whenthe string 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.

Explanation / Answer

If the tension is constant, the speed of the wave on the string isconstant, so the length is inversely proportional to thefrequency. Fret zero is the full length, right? So fret one is that full length divided by 2^(1/12). Fret two is the full length divided by 2^(2/12). The length to fret n is : L(n) = total length * 2^(n/12) Calculate L(0) (trivial), L(1), L(6), and L(7), and do thesubtractions.

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