Problem

The frequency of a music note in relation to a specific note is modeled by the following function.
\[
F(x)=F_{0}(1.059463)^{*}
\]

Here, $F_{0}$ is the reference frequency and $x$ is the number of half steps up from $F_{0}$.
The frequency of the note $A_{3}$ is $220 \mathrm{~Hz}$. Find the frequency of the note $A$ A. which is I half step above $A_{3}$. Round to the nearest whole number.

Answer

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Answer

\(\boxed{233}\) Hz is the frequency of the note one half step above $A_{3}$.

Steps

Step 1 :The problem provides the frequency of the note $A_{3}$ as 220 Hz and asks for the frequency of the note one half step above $A_{3}$. The formula given to calculate this is $F(x)=F_{0}(1.059463)^{*}$, where $F_{0}$ is the reference frequency and $x$ is the number of half steps up from $F_{0}$.

Step 2 :We can substitute the given values into the formula. Here, $F_{0}$ is 220 and $x$ is 1.

Step 3 :By substituting these values into the formula, we get $F(1)=220(1.059463)^{1}$.

Step 4 :Solving this equation gives us the frequency of the note one half step above $A_{3}$ as approximately 233 Hz.

Step 5 :\(\boxed{233}\) Hz is the frequency of the note one half step above $A_{3}$.

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