Problem 12.43 Part D Determine the fourth fret. position of the Express your ans
ID: 1658148 • Letter: P
Question
Problem 12.43 Part D Determine the fourth fret. position of the Express your answer to one decimal place and include the appropriate units. When a player's finger presses a guitar string down onto a fretthe length of the vibrating portion of the string is shortened, thereby increasing the string's fundamental frequency (Figure 1). The string's tension and mass per unit length remain unchanged. If the unfingered length of the string is L = 65.0 cm, determine the positions at of the first six frets, if each fret raises the pitch of the fundamental by one musical note compared to the neighboring fretOn the equally tempered chromatic scale, the ratio of frequencies of neighboring notes is 1/12 H . hn O ? , _ Value Units Submit My Answers Give Up Submit Part E Determine the position 2 of the fifth fret. Figure 1 of 1 Express your answer to one decimal place and include the appropriate units. a 9 ? 'H A n o - _ Value Units . L5 | Submit My Answers Give Up Part F Determine the position 1 of the sixth fret.Explanation / Answer
Given that,
L = 65 cm
Ration of frequencies, f / f1 = 2(1/12)
we know that,
L = v / 2f
L1 = v / 2f1
L1 / L = (f / f1)
Position x for first fret,
x1 = (f / f1)*L - L
x1 = 2(1/12) *65 - 65
x1 = 3.86 cm
x2 = 2(1/12) *68.86 = 72.9 cm
x2 = 7.95 cm
x3 = 2(1/12) * 72.9 - 65 = 77.3 cm
x3 = 12.3 cm
(D)
x4 = 2(1/12) * 77.3 = 82 cm
x4 = 17 cm
x4 = 17 cm
(E)
x5 = 2(1/12) *82 = 86.8 cm
x5 = 21.8 cm
(F)
x6 = 2(1/12) * 86.8 = 92 cm
x6 = 27 cm