find the spacing between the string

Physics
Tutor: None Selected Time limit: 1 Day

Apr 6th, 2015

frequency = (1 / (2 * L)) * root (T / u) 

f = k / L  where k= constant

 the factor of the twelfth root of 2=1.059463=b

shifting up in frequency by 1 semitone when it is fingered to touch the first fret, its length changes to

length=0.628 / 1.059463 = 0.628 / b 

 j th fret the length will given by 0.628 / b^j

 for the j+1 fret,length=0.628 / b^(j + 1) 

 distance between the frets is:

(0.628 / b^j) - (0.628 / b^(j+1)) 
= 0.628 * (1/b^j - 1/b^(j+1)) 
= 0.628 * (b^(j+1) - b^j) / (b^j * (b^(j+1)) 
= 0.628 * b^j * (b - 1) / (b^j * (b^(j+1)) 
= 0.628 * (b - 1) / b^(j+1) 
= 0.037343 / 1.059463^(j+1) m 
= 3.7343 / 1.059463^(j+1) cm 

a) Between fret 4 and 5, j = 4

 spacing =3.7343 / 1.059463 ^ 5 
  = 2.7976 cm 

b) Between fret 9 and 10, j = 9

  spacing =3.7343 / 1.059463^10 
    = 2.0958 cm

Apr 6th, 2015

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Apr 6th, 2015
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