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iogann1982 [59]
3 years ago
5

1. Determine the distance from the bridge for three consecutive frets. Round each answer to 3 decimal place. For example, you ca

n calculate the distance from the bridge for the 4th, 5th and 6th fret.
2. Create the ratios of the highest fret to the previous fret and simplify to a decimal. Create the ratio of the next highest fret to the previous fret and simplify to a decimal. What are the values? For example, if your calculated the distance to the 4th, 5th and 6th fret, you would create the two ratios: 6th fret distance/5th fret distance, and 5th fret distance/4th fret distance. How are these ratios two related? Does this remind you of something we studied earlier in the course?
Mathematics
1 answer:
Virty [35]3 years ago
3 0

The distance of each subsequent  fret from the bridge is constant multiple

of the distance of the previous fret from the bridge.

  • Distance from the bridge for the 4th fret is approximately <u>55.185 cm</u>
  • Distance from the bridge for the 5th fret is approximately <u>52.087 cm</u>
  • Distance from the bridge for the 6th fret  is approximately <u>49.164 cm</u>

<u />

Reason:

1. The equation for the distance of the x-th fret from the bridge in

centimeters is given as follows;

  • d = 21.9 \times \left(2\right)^{\frac{20 - x}{12} }

Therefore, for three consecutive frets, we have;

At \ the \ 4th \  fret; \ d = 21.9 \times \left(2\right)^{\frac{20 - 4}{12} } \approx 55.185

The distance from the bridge for the 4th fret = <u>55.185 cm</u>

At \ the \ 5th \  fret; \ d = 21.9 \times \left(2\right)^{\frac{20 - 5}{12} } \approx 52.087

The distance from the bridge for the 5th fret = <u>52.087 cm</u>At \ the \ 6th \  fret; \ d = 21.9 \times \left(2\right)^{\frac{20 - 6}{12} } \approx 49.164

The distance from the bridge for the 6th fret = <u>49.164 cm</u>

<u />

2. The ratio are;

  • \dfrac{Distance \ to \ the \ 6th \ fret }{Distance \ to \ the \ 5th \ fret} = \dfrac{49.164}{52.087} = \dfrac{21.9 \times \left(2\right)^{\frac{14}{12} }}{21.9 \times \left(2\right)^{\frac{15}{12} }} =e^{\dfrac{1}{\dfrac{Ln(2)}{12} } }
  • \dfrac{Distance \ to \ the \ 5th \ fret }{Distance \ to \ the \ 4th \ fret} = \dfrac{52.087}{55.185} =  \dfrac{21.9 \times \left(2\right)^{\frac{15}{12} }} {21.9 \times \left(2\right)^{\frac{16}{12} }} =e^{\dfrac{1}{\dfrac{Ln(2)}{12} } }

Therefore, the ratio of the distances of each fret to the distance of the

previous fret is a constant, which is similar to a geometric progression.

Therefore;

The distances of the frets from the bridge form a <u>geometric </u>

<u>progression</u> or sequence.

Learn more here:

brainly.com/question/25244113

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