Question

23 multiple choice 2 points the note that is d above middle c has a frequency of approximately 293.7. what is the frequency of the next highest semitone?

Explanation:

Step1: Recall the formula for frequency of a semitone

The formula for the frequency \(f_{n + 1}\) of a note that is one semitone higher than a note with frequency \(f_n\) is \(f_{n+1}=f_n\times2^{\frac{1}{12}}\).

Step2: Substitute the given value

Given \(f_n = 293.7\), then \(f_{n + 1}=293.7\times2^{\frac{1}{12}}\).
We know that \(2^{\frac{1}{12}}\approx1.05946\).
So \(f_{n + 1}=293.7\times1.05946\).

Step3: Calculate the product

\(293.7\times1.05946=(300 - 6.3)\times1.05946=300\times1.05946-6.3\times1.05946\)
\(300\times1.05946 = 317.838\), \(6.3\times1.05946=6.674598\)
\(f_{n + 1}=317.838- 6.674598=311.163402\approx311.1\)

Answer:

The frequency of the next - highest semitone is approximately \(311.1\)