Assuming that the tension in the string is the same for any note, find the spaci

label Physics
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Apr 4th, 2015

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: λ = 2L, 
and the frequency ratio can be written as: 

f'/f = 2L/(2L-d) = 2^(1/12) = 1.059 

2L = 2*0.628 = 1.256 m 

1.256/(1.256-d) = 1.059 

d = 1.256 - (1.256/1.059) = 0.07 m 

b) fret 7 corresponds to ⅓ L = ⅓ 0.628 = 0.209 m 

λ = 2L' = 2*0.209 = 0.418 m 

2^(1/12) = 0.418/(0.418-d) 

d = 0.418 - 0.418/1.059 = 0.141 m

Apr 3rd, 2015

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