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 2 and fret 1
1 cm and
(b) between fret 7 and fret 6
Spacing between frets of a guitar are calculated for desired notes.