As the drawing shows, the length of a guitar string is L = 0.508 m. The frets ar

Question

As the drawing shows, the length of a guitar string is L = 0.508 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 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 1 and fret 0 and (b) between fret 7 and fret 6.

Explanation / Answer

The frequency ratio corresponding to the interval between each consecutive semitone is 2^(1/12). Since the tension and density of the string is constant, then the wave speed in the string is constant and the wavelengths for a stretched string is given by: ? = 2L, and the frequency ratio can be written as: f'/f = 2L/(2L-d) = 2^(1/12) = 1.059 2L = 2*0.575 = 1.15 m 1.15/(1.15-d) = 1.059 d = 1.15 - (1.15/1.059) = 0.064 m b) fret 7 corresponds to ? L = ? 0.575 = 0.192 m ? = 2L' = 2*0.192 = 0.383 m 2^(1/12) = 0.383/(0.383-d) d = 0.383 - 0.383/1.059 = 0.021 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.