Question

Here is the Question, I appreciate the help:

Louise is building a guitar-like instrument. It has small metal bars, called frets, positioned across its neck so that it can produce notes of a specific scale on each string. The distance a fret should be placed from the bridge is related to the string’s root note length by the function d(n) = r ( 2^-n/12), where r is the length of the root note string and n is the number of notes higher than the string’s root note. Louise wants to know where to place frets to produce notes on a 50-cm string.
1 . Find the distance from the bridge for a fret that produces a note exactly one octave (12 notes) higher than the root note .

a . Substitute values for r and n in the given function .

b . How far from the bridge should the fret be placed?

c . What fraction of the string length is the distance of this fret from the bridge?

Answer 1

Given formula is

d(n) = r ( 2^-n/12)

So just put the given values

d(12) = 50(2^-12/12)

d(12) = 50(2^-1)

d(12) = 50*0.5

d(12) = 25 cm

fraction of the string length is the distance of this fret from the bridge

25/50 = 1/2