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問題

解法ステップ

1. Understand the question
   1. math on the spot frets are small metal bars positioned across the neck of a guitar so that the guitar can produce the notes of a specific scale. to find the distance a fret should be placed from the bridge, multiply the length of the string by $2^{-\frac{n}{12}}$, where $n$ is the number of half steps higher than the strings root note. where should a fret be placed to produce an a flat note on the e string (four half steps higher)? 64 cm
2. Explanation

   Step1: Identify given values

   String length $L = 64$ cm, $n = 4$

   Step2: Apply the given formula

   The distance formula is $\text{Distance} = L \times 2^{-\frac{n}{12}}$
   Substitute values: $\text{Distance} = 64 \times 2^{-\frac{4}{12}} = 64 \times 2^{-\frac{1}{3}}$

   Step3: Calculate the value

   First, $2^{\frac{1}{3}} \approx 1.26$, so $2^{-\frac{1}{3}} \approx \frac{1}{1.26} \approx 0.7937$
   Then $\text{Distance} \approx 64 \times 0.7937 \approx 50.8$ cm

3. Final answer

   The fret should be placed approximately 50.8 cm from the bridge.

答え

Question Analysis

OCR Text

10. math on the spot frets are small metal bars positioned across the neck of a guitar so that the guitar can produce the notes of a specific scale. to find the distance a fret should be placed from the bridge, multiply the length of the string by $2^{-\frac{n}{12}}$, where $n$ is the number of half steps higher than the strings root note. where should a fret be placed to produce an a flat note on the e string (four half steps higher)? 64 cm

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