Question

How to solve this problem? (the answer is 262 Hz). i want to know the step by step on how to solve the equation given. if it helps, i am a grade 10 student. (YES, this is a MATH problem)

Answer 1

Answer:

The frequency of middle C = 262 Hz

Step-by-step explanation:

The formula for calculating the frequency, F hertz, of a note n seminotes above the concert pitch is:

`F\text{ = 440(}\sqrt[12]{2})^n`

This can be re-written as:

`F=440(2^{(n)/(12)})`

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

`\begin{gathered} F=440(2^{(-9)/(12)}) \\ F\text{ = 440(}0.5946) \\ F\text{ = }261.62\text{ Hz} \\ F\text{ = 262 Hz (to the nearest hertz)} \end{gathered}`

The frequency of middle C = 262 Hz