Question

A guitar player can change the frequency of a string by "bending" it-pushing it along a fret that is perpendicular to its length. This stretches the string, increasing its tension and its frequency. The high E string on a guitar is 64 cm long and has a tension of 74 N. The guitarist pushes this string down against a fret located at the center of the string, which gives it a frequency of 659 Hz.He then bends the string, pushing with a force of 4.0 N so that it moves 8.0 mm along the fret.

What is the new frequency?

Answer 1

frequency, f = sqrt(T/(m/L)) /2L

659 = sqrt(74/(m/0.64)) /(2 x 0.64)

843.52 = sqrt(47.36/m)

mass, m = 6.66 x 10^-5 kg

T' = 74 + 4 = 78 N

L' = 64 + 0.8 = 64.8 cm

f' = sqrt(78/(6.66 x 10^-5/0.648))/(2 x 0.648)

f' = 672.39 hz

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