Piano Frequency

Problem Statement

There are 52 white keys on a piano.
The frequency of each key is the number of vibrations per second the key's string makes.
Is this relation a function? If not, explain why.
If so, predict an equation that models the data.

 Key Position 1 8 15 22 29 36 43 Frequency 27.5 55 110 220 440 880 1760

Source: Bellman, A. et. al, (no date) Algebra. Nedham, MA: Prentice-Hall.

Investigation/Exploration of the Problem

In order to find whether or not the relation is a function and predict an equation that models the data we can use a spreadsheet. (Click here for the spreadsheet).

A function is defined as a rule of matching elements of two sets of numbers in which an input value from the first set has only one output value in the second set. We see that this relationship is a function because each element in the range (y) is assigned to a unique value in the domain. We also see that the equation that models the data in this case is

y = 24.907e0.099x
R2 = 1

Because R2 = 1, we know that this equation is very accurate and will model the data very accurately.

Extensions of the Problem

To extend this problem, we can find the frequency of all 52 keys using the equation  y = 24.907e0.099x by using a spreadsheet. Click here for spreadsheet.

Author & Contact
Laura Thomas

Memorial Middle School

Conyers, GA
LThomas@rockdale.k12.ga.us