 Department of Mathematics Education

Jim Wilson, EMAT 6680

## Exporations with the String Data Set

The data set is generated by measuring the lengths along a guitar string from each fret to the bridge. Most guitars will have 20 to 22 frets.

Things to try

1. Make a graph. In this graph the y-axis gives the lengths measured in centimeters and the x-axis gives the number of the fret.

2. Build a spreadsheet table with Fret number in the A column and the measures in the B column. Excel file for String Data

3. In Column C, compute the ratio or successive cells in Column B. That is, place B2/B1 in C2. Then drag down from C2 to C23 (or to the last data entry). Observation? Interpret?

4. Experimentally, in step 3 we note that the successive terms in Column B are approximately in the same ratio. We can obtain a better estimate of this common ratio by taking the arithmetic mean of the entries in Column C.

5. Now, use this ratio R, to write a funtion and generate values for the lengths of the string from Frets 0 - 22 using the the function.

6. How will the graph change if the instrument has a shorter neck? For instance, what if the length of the string from Fret 0 (the nut) is 50 cm?

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