Answer:
The frequency of middle C = 262 Hz
Explanation:
The formula for calculating the frequency, F hertz, of a note n seminotes above the concert pitch is:
[tex]F\text{ = 440(}\sqrt[12]{2})^n[/tex]
This can be re-written as:
[tex]F=440(2^{\frac{n}{12}})[/tex]
Middle C is 9 semitones below the concert pitch
That is, n = -9
To find the frequency of middle C, substitute n = -9 into the equation for F
[tex]\begin{gathered} F=440(2^{\frac{-9}{12}}) \\ F\text{ = 440(}0.5946) \\ F\text{ = }261.62\text{ Hz} \\ F\text{ = 262 Hz (to the nearest hertz)} \end{gathered}[/tex]
The frequency of middle C = 262 Hz
