In assignment twelve we used a spreadsheet to develop a nice way to compute the common ratio in a geometric series using musical instruments. On a spreadsheet one can show the data entered as they measured from the zero fret to the base of a guitar. I will give the data we used followed by a lab for the classroom.
Enter the following data on a spreadsheet such as ClairsWorks then calculate the ratio from item B2/B1. This will give a very close approximation to the common ratio is the measuring has been done carefully.
Column A - Number of the fret 0, 1,2,3,... 20
Column B - Length 64.8, 61,57.5,54.5,51.5,48.5,45.8,43, 40.8, 38.5,30.5,34.4,32.5,30.6,28.8,27.1,25.8,24.4,23,21.8,20.7
Common ratio is approximately .94
Working in teams of four, two people should measure and check each other as you go through the exercises. One person should call out the data to the data entry person and double check the data entry. One person should enter the data on Clairsworks spreadsheet in the following manner. Column A should be the fret number beginning with 0 as the open fret( the longest measurement). Column B should be the measurement of the length of the guitar string from the fet to the bridge of the guitar. Take these measurements in centimeters. Be as accurate as possible. After recording this information use column C to calculate the ratio of B2/B1, B3/B2, etc. Record your observations below.
1. What type of sequence appears to be illustrated by the different lengths? Indicate how your group determined this ( approximating is allowed in real data collection).
2. Are there any data point which do not seem to "fit" the others? How could this be explained?
3. Select columns A and B and create a graph by using the "Make a Chart" menu. Under " Make a Chart" select the XY scatter plot. Next modify the axes indicating that the X values are the fret numbers and the y values are the lengths measured. Below make a sketch of the graph. Discuss how you might interpret what you are seeing.
4. Compare the lengths of the fret numbers that are approximately half of one another. What is trye about these lengths?
5. Find the sum of all the numbers in the column C and divide by the number of frets to find a more accurate constant ratio.
6. Print your spreadsheet and graph.
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