As a luthier, you make high-quality guitars for which accurate fret placement is crucial. Referring to the figure below, we think of the nut itself as fret O. Additional frets are numbered as we move from the nut toward the saddle. String Pegs Saddle Sound Hole Body Bridge Pickguard n = fret number 0 1 2 3 4 Neck 23.60 22.27 21.02 19.84 Head Fretboard Stock Frets 900 Nut The following table shows the distance D(n), in inches, from the saddle to the nth fret. D = distance to saddle, in inches 25.00 Tuners (Machine Heads, Tuning Keys, Tuning Machines, Pegheads) (a) Show that the data are exponential. Because in increases by 1 each time, to show that the data are exponential, we must show that the successive ratios (rounded to two decimal places) are the same. Because all of the ratios are equal to the data are exponential. (b) Make an exponential model D that shows the distance from the nth fret to the saddle. Use the ratio found in part (a). (Rounding causes variation from the correct model D = Sx 2-n/12, where S is the scale length of the guitar. Also, for technical reasons, fret placement is measured from the nut rather than the saddle.) D(n) = (c) According to your model, how far (in inches) is it from the fifth fret to the sixth fret? (Round your answer to two decimal places.) in
As a luthier, you make high-quality guitars for which accurate fret placement is crucial. Referring to the figure below, we think of the nut itself as fret O. Additional frets are numbered as we move from the nut toward the saddle. String Pegs Saddle Sound Hole Body Bridge Pickguard n = fret number 0 1 2 3 4 Neck 23.60 22.27 21.02 19.84 Head Fretboard Stock Frets 900 Nut The following table shows the distance D(n), in inches, from the saddle to the nth fret. D = distance to saddle, in inches 25.00 Tuners (Machine Heads, Tuning Keys, Tuning Machines, Pegheads) (a) Show that the data are exponential. Because in increases by 1 each time, to show that the data are exponential, we must show that the successive ratios (rounded to two decimal places) are the same. Because all of the ratios are equal to the data are exponential. (b) Make an exponential model D that shows the distance from the nth fret to the saddle. Use the ratio found in part (a). (Rounding causes variation from the correct model D = Sx 2-n/12, where S is the scale length of the guitar. Also, for technical reasons, fret placement is measured from the nut rather than the saddle.) D(n) = (c) According to your model, how far (in inches) is it from the fifth fret to the sixth fret? (Round your answer to two decimal places.) in
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:As a luthier, you make high-quality guitars for which accurate fret placement is crucial. Referring to the figure below, we think of the nut itself as fret O. Additional frets are numbered as we move
from the nut toward the saddle.
String
Pegs Saddle Sound Hole
Body Bridge Pickguard
n = fret number
0
1
2
3
4
Neck
23.60
22.27
21.02
19.84
Head
Fretboard Stock
Frets
900
Nut
The following table shows the distance D(n), in inches, from the saddle to the nth fret.
D = distance to
saddle, in inches
25.00
Tuners
(Machine Heads,
Tuning Keys,
Tuning Machines,
Pegheads)
(a) Show that the data are exponential.
Because in increases by 1 each time, to show that the data are exponential, we must show that the successive ratios (rounded to two decimal places) are the same. Because all of the ratios are
equal to
the data are exponential.
(b) Make an exponential model D that shows the distance from the nth fret to the saddle. Use the ratio found in part (a). (Rounding causes variation from the correct model D = Sx 2-n/12, where
S is the scale length of the guitar. Also, for technical reasons, fret placement is measured from the nut rather than the saddle.)
D(n) =
(c) According to your model, how far (in inches) is it from the fifth fret to the sixth fret? (Round your answer to two decimal places.)
in
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