Texas Mathematics Teacher Spring/Summer 2022 - 16

On the Cover: Find the Mathematics... in Musical Instruments!
How many ways can a player press all 4 valves? exactly 3
valves? exactly 2 valves? exactly 1 valve? 0 valves?
How many total ways can a player press the valves of a
tuba?
A recorder has 8 finger holes, and a player can cover the
holes to change the sound made by the recorder. How
many total ways are there to cover the holes of a recorder?
9th to 12th Grade
To change the sound coming from a trombone, the player
lengthens or shortens the slide, which changes the distance
that the air must travel to exit the trombone. Eli collected
data with his trombone. He measured the distance
that he extended the slide from the starting point (known
as first position), and the frequency of the sound. Here is
his data.
Distance of slide
extension
(centimeters)
9.5
15
25
34.7
46.5
59.5
Frequency of
sound
(Hertz)
174
164
155
146
138
130
123
Use technology to create a scatterplot of the data.
Does this relationship appear to be linear?
Is there a positive or negative correlation? Is the correlation
strong or weak?
If Eli wanted a frequency of 150 Hertz, what should the
distance of the extension be?
Why does it not make sense to extrapolate based on this
data set?
To change the sound coming from a guitar string, the
player presses on a string to change its length. Eli also collected
data with his guitar. He measured the length of the
string and the frequency of the sound. Here is his data.
Length of
string
(centimeters)
65
61.7
55
49
43.9
39.2
37
34.8
16 | Spring/Summer 2022
Frequency of
sound
(Hertz)
82
87
98
110
123
130
146
164
Texas Mathematics Teacher
Dusty Jones
DLJones@shsu.edu
Professor
Sam Houston State University
Use technology to create a scatterplot of the data.
Does this relationship appear to be linear?
Is there a positive or negative correlation?
Is the correlation strong or weak?
If Eli wanted a frequency of 150 Hertz, how long
should the string be?
Would it make sense to extrapolate based on this
data set?
Continued on page 23

Texas Mathematics Teacher Spring/Summer 2022

Table of Contents for the Digital Edition of Texas Mathematics Teacher Spring/Summer 2022

Texas Mathematics Teacher Spring/Summer 2022 - 1
Texas Mathematics Teacher Spring/Summer 2022 - 2
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Texas Mathematics Teacher Spring/Summer 2022 - 35
Texas Mathematics Teacher Spring/Summer 2022 - 36
http://www.brightcopy.net/allen/txmt/68-01
http://www.brightcopy.net/allen/txmt/67-01
http://www.brightcopy.net/allen/txmt/66-02
http://www.brightcopy.net/allen/txmt/66-01
http://www.brightcopy.net/allen/txmt/65-02
http://www.brightcopy.net/allen/txmt/65-01
http://www.brightcopy.net/allen/txmt/64-02
https://www.nxtbook.com/allen/txmt/64-1
https://www.nxtbookmedia.com