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
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The solution is attached below in two files. the files are identical in content, only ...
The solution shows how to derive the expression for the distances between consecutive frets of a guitar.