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THESIS

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This is to certify that the

thesis entitled

The Physics of Sound and Music
presented by
Eric Pulver

has been accepted towards fulfillment
of the requirements for

 

 

Master of degree In Physical
Science Science

fl/a/QZW

Major professor

Date July 21, 1998

 

0-7639 MS U is an Affirmative Action/Equal Opportunity Institution

 

 

LIBRARY

MIChlgan State
UnIversIty

 

 

 

PLACE IN RETURN BOX
to remove this checkout from your record.
TO AVOID FINES return on or before date due.

 

DATE DUE MTE DUE

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use chIRCJDatoDuopGS-p.“

THE PHYSICS OF SOUND AND MUSIC
By

Eric J. Pulver

OF A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

DIVISION OF SCIENCE AND MATHEMATICS EDUCATION
1998

Professor Merle K. Heidemann

ABSTRACT
THE PHYSICS OF SOUND AND MUSIC
By

Eric J. Pulver

Students in physics classes did not appear to understand some of the basic concepts
of wave mechanics, such as how and why waves move, wave types, and wave interference.
Since sound is a wave phenomenon not utilized in the existing curriculum, a new unit on
sound and music was developed to supplement the existing wave unit and reinforce these
concepts. Through pre-test and post-test essays, subjects were quantitatively evaluated on
their improvement in these conceptual areas after participating in the new unit. The sound
and music unit itself was also qualitatively evaluated, as this was its first implementation.
Overall, student understanding was increased due to the additional experiments and other

activities provided in the sound and music unit.

ACKNOWLEDGMENTS

I would like to Show appreciation to the following people for all of their personal and
professional support:
Beth - my friend, my partner, my primary source of inspiration.
Marvin and Sharyl Pulver - my parents, they have made me who I am - literally.
Larry Burgess and David Foy - mentors and friends who help me become a better
person and a better teacher.
Jefl‘ Chomey, David Dean, David McCreight, and David Novak - physics geeks.
Merle Heidemann, Clarence Suelter, Sharon Snyder, Bill Hartmann and all other

MSU personnel associated with the DSME

iii

TABLE OF CONTENTS

Bag:
List of Tables .................................................... vi
List of Figures ................................................... vii
Introduction
The Problem and the Pedagogy ................................. 1
Scientific Background ........................................ 3
Demographics of Subjects ..................................... 5
Implementation of Unit ............................................. 8
Evaluation of Unit
Overview ................................................. 15
Quantitative Data
Question 1 ........................................... 16
Question 2 ........................................... 17
Question 3 ........................................... 18
Question 4 ........................................... 19
Question 5 ........................................... 21
Question 6 ........................................... 22
Qualitative Data ............................................ 23
Analysis of Data ............................................ 26
Conclusion ...................................................... 29
Appendices
Appendix A: Experiments and Activities .......................... 32
Experiment #1: Speed of Sound in Air ...................... 33
Standing Wave Demonstration ........................... 34
Experiment #2: Temperature and the Speed of Sound .......... 35
Resonance Worksheet #1: The Air Column .................. 36
Experiment #3: Vibrating Strings ......................... 37
Resonance Worksheet #2: The Vibrating String ............... 38
Music Worksheet #1: The Notes .......................... 39
Musical Scale for 4 Octaves ............................. 40
Music Worksheet #2: The Harmonies and Chords ............. 41
Sound and Music Quiz ................................. 42

iv

Appendix B: Assessment Rubric ................................ 44
Appendix C: Table 1: Student Data gathered from pre- and post-test . . . . 47

References ...................................................... 52

47...

27...

27...

28.

LIST OF TABLES

Table 1: All data gathered from pre-test and post-test
Table 2: Average Pre- and Post-test Scores for All Students

Table 3: Average Pre- and Post-test Scores for Female Subjects

. . Table 4: Average Pre- and Post-test Scores for Male Subjects

10...

12...

17...

18...

19...

21...

22..

23...

25..

26...

LIST OF FIGURES

. Figure 1: Representation of air molecules vibrating. Crests are areas of high

pressure and molecular density. Troughs are areas of low pressure and molecular

density.

. Figure 2: Relative frequencies of musical notes

. Figure 3: Steps to solve mathematically based problems.

Figure 4: Resonance occurs in a column of air by creating an antinode at an open
end. Represented here by the transverse wave model (which students understand
more easily) and the more accurate longitudinal wave, due to air pressure
difi‘erences.

Figure 5: Tone Intervals in the Just Scale and Equally Tempered Scale

Figure 6: Histogram of Pre-test and Post-test Scores for Question 1.

Figure 7: Histogram of Pre-test and Post-test Scores for Question 2.

Figure 8: Histogram of Pre-test and Post-test Scores for Question 3.

Figure 9: Histogram of Pre-test and Post-test Scores for Question 4.

. Figure 10: Histogram of Pre-test and Post-test Scores for Question 5.

Figure 11: Histogram of Pre-test and Post-test Scores for Question 6.

. Figure 12: “Box and Whiskers” plot showing the distribution of scores. Each

segment represents 25% of the scores.
Figure 13: Pie Chart Representing the Changes in Score. Each Area Represents

the Number of Students Whose Score Changed by the Amount listed.

vii

Introduction
The Problem and The Pedagogy

Physics teachers at Holt High School have been utilizing primarily the same
curriculum for decades. This experiment-based method of instruction has been powerful at
helping students understand the basics of physics. In the years I have taught, however, I have
found the unit on waves to be less effective than the other units in the course. Students in the
past didn’t seem to understand some of the basic concepts of wave mechanics, including how
or why waves move, wave types, and wave interference. Although some of these topics were
taught in earlier courses which specifically address Michigan Essential Goals & Objectives for
Science Education outcomes for waves (Objectives 17, 18, & 20 - MEGOSE, 1991), students
just did not fully understanding these concepts.

In the summer of 1997, through a course of study with the Division of Math and
Science Education within the College of Natural Science at Michigan State University, I
developed a unit which intended to address the shortcomings of the Holt physics curriculum.
I called on the experience of others to help develop several of the activities which came from
this research time. In addition to MSU personnel, several of the other physics teachers
involved with the DMSE had experience with units involving sound waves. These discussions
ultimately led to an experiment-based unit which would be consistent with my teaching
technique and philosophy.

“We cannot merely give students a new concept or understanding. All teachers can
do is create an environment where that particular concept or idea is available for exploration,

analysis, and consideration.” (Penick, 1996). It is through experimentation that students

primarily gain their understanding. In the past, shallow glass-bottomed water containers
known as ripple tanks had been used to project images of actual waves onto a screen below
the tank. These are very effective and important tools in helping students see and test the
waves in action. Observations of the visible and tangible ripples in the water were not
complete enough, however, especially when dealing with the more advanced wave concepts
such as difli‘action patterns of light. Students had trouble because they didn’t understand the
fundamental elements of wave mechanics. In order to encourage better student understanding
of the basics, another wave phenomenon needed to be studied - sound.

Studying sound in the high school physics class is not a novel idea; in fact, it is the
topic of a chapter in most high school physics textbooks. At Holt High School, however, the
PSSC (Physical Science Study Committee) Physics textbook which has been used since the
early 1960's does not include sound as part of its curriculum, so this new unit described in this
document, teaching the physics of sound and music, would be a first attempt.

The sound unit followed the wave units which had worked well in the past and was
implemented as an additional unit. Students performed experiments on wave propagation,
wave reflection, superposition, wave speed, refraction of waves, diffraction and interference
with Slinky°s and the ripple tanks. In this way, the sound unit used background information
and utilized scientific method, which “is a system of thought that deals with concepts which
flow out of relevant facts. The process cannot be implemented without explanation of facts
and the use of basic skills.” (Grarnbs, 1991). The sound unit reinforced many of the skills
learned in the previously performed ripple tank experiments by studying wave properties in

a different medium before moving on to the more complicated topics requiring understanding

of waves.

A firrther supplement to the sound unit, an investigation into musical notes and chords
as they relate to wave mechanics, is a topic not traditional in the high school physics
classroom. Music does, however, lend itself quite nicely as an extension of the sound unit and
is of interest to many high school physics students. An untested, secondary purpose of this
part of the unit was to offer an attraction which would entice more students into pursuing
physics, perhaps those who wouldn’t ordinarily consider participating in the elective physics
and chemistry courses. Increasing the appeal for courses with a stigma that has plagued them
for years should result in more students being introduced to the world of science.

The evaluation process of this unit was primarily through a pre- and post-tests, but
other, more subjective assessment techniques were also implemented with the focus of the
evaluative process being student understanding of concepts. The course was not restructured
and students would still perform experiments, discuss findings and draw conclusions based
on the collected data. Since there were to be no new instructional methods attempted, the
purpose of the unit was to give students another set of phenomena from which to learn the
concepts of wave mechanics.

Scientific Background

Sound waves are longitudinal waves which move through air. Longitudinal waves are
the oscillations of molecules in the direction of transmission. As with any wave, sound
moves in a straight path fiom its source at a constant speed, reflects from barriers, changes
speed and direction (refracts) when changing media, spreads (diffracts) around objects and

through openings, and follows the principle of superposition. In superposition, waves of the

same type (sound, light, etc.) in the same medium will combine displacements where they
meet. In other words, a crest which meets a crest will add to form a larger crest, and a trough
and a crest will combine to form a position of no disturbance in the medium.

Sound waves are the result of a vibration in the medium of transmission. For example,
in air, the molecules are disturbed with enough energy to continue the agitation to the
adjacent particles. A significant disturbance will travel through many molecules. This

disturbance results in changes in air pressure.

 

Areas of hi er ressure are where more Crest T
gh p z: o. o :.:o . . 3. . 30. rough 3;.
.00 .0 O
molecules have been pushed together - these 3:: . '. :0 .0 0 3:: 0 :03. . :a .
”.E.. o :g‘o 0 ‘0'.“ ‘::o . 0 .0
are the crests of the longitudinal wave. :3. . 0.4. , g... . :3: ' '. o :35- ’
ole '0‘ o ... 0.... .$.o

 

 

 

Figure 1 Shows the dIStnbunon Of a" Figure 1: Representation of air molecules vibrating.
Crests are areas of high pressure and molecular
molecules when a sound wave propagates density. Troughs are areas of low pressure and

molecular density.
through them. When these disturbances
reach a human ear, the tympanic membrane oscillates sympathetically with the changes in air
pressure causing the person to sense the sound. The more fi'equent the oscillation, the higher
the pitch that is perceived.

A standing wave is formed when a wave reflects back on itself and, through
superposition, causes some locations to oscillate between crests and troughs (antinodes),
while other positions show no disturbance in the medium (nodes). The nodes are areas of
destructive interference and the antinodes are areas of constructive interference. The standing

wave is a fundamental component in making music. A standing wave is produced in wind

instnrments by vibrating a column of air in the instrument. A stringed instrument creates a

standing wave when vibrating with nodes at each connected end of the string. Rods, plates
and bells - the other categories of musical instruments - also work in the same fashion.
“Of the many principles taught in elementary physics courses, almost every one is
reducible to a mathematical statement.” (Sutton, 193 8). The musical scale is no exception.
It is based on frequencies of sound waves. The A string on a violin, which has 440 vibrations
per second is commonly used for “standard pitch,” although some musicians use the middle

C on the piano. Scientists generally use A4,,0

 

 

as standard pitch. The scale of musical

notes is developed fi'om the standard pitch

 

 

 

 

 

 

 

 

based on simple whole number ratios as

 

 

 

 

 

 

 

 

 

 

 

 

 

 

shown in Figure 2. Musical “Utes are Emmi“: 8:9 9:10 15:16 8:9 9:10 8:9 15:16 8:9

 

. Figure 2: Relative frequencies of musical notes
pleasrng to hear together when, through

superposition, they create a simple wave pattern - these are called harmonies. The discordant
sounds, which are not pleasing to the ear, are caused when waves combine to create a
complex repeating wave pattern.
Demographics and Academic Profile of the Subjects

The community in which this study occurred is a suburban community. Holt is largely
a “bedroom community” with most residents commuting to work at nearby General Motors
manufacturing plants, state government facilities, and the local university. This once rural
area maintains very little ethnic diversity. The high school houses over eleven hundred
students and slightly fewer than one hundred teachers, administrators, and support stafl‘. The

students who were the subjects of this course of study were one-hundred-five high school

students consisting of four juniors, one-hundred-one seniors of which sixty-three were males
and forty-two females. There were seven blacks, six Asians, and ninety-two whites, mostly
from middle or upper-middle class homes, all of whom had signed up for the elective, senior-
level physics course. The students studied were in five separate classes with each receiving
the same instruction and being assessed on the same criteria. All of these students expect to
graduate from high school and the majority plan to attend colleges or universities.

Most of the students in these classes had passed advanced algebra and many were
taking either a functions and trigonometry based course called “Pre-Calculus,”or the advanced
placement calculus course. “Students must be taught mathematical skills for solving problems
in physics. It cannot be assumed that a student who has studied trigonometry and algebra can
automatically master all of the skills

and knowledge required to solve W
I. Read the problem

physics problems.” (W ashton, 2. Write down what you know
3. Write down what you don 't know - what is the

 

1960). Therefore, many classroom problem asking for?

4. Find the correct equation to use and write it
hours had been dedicated early in down.

5. Rewrite the equation with the correct numbers
the school year enhancing the in it and solve it.

6. Write the answer down with the correct units.

 

 

 

smdents prOblem'SOIvmg Skills Figure 3: Steps to solve mathematically based problems. Taken

, . . from Adamovic & Hedden, 1997.
usrng the process shown m Figure 3

to make the problem solving-process second nature for the students. This ensured
mathematics competency by students for the study of more conceptually complicated topics.
The sound unit was introduced in the course after about twenty five weeks into the

forty week school year. By this time, the students had worked together for no less than one

quarter of the school year and in most cases three quarters of the school year. Students had
already worked through units involving extensive experimentation with kinematics, light and
optics, as well as waves. Thus, the students had formed their own work groups and
established roles within the group structure. Some students prefer to be hands-on with the
experiments, while others would rather “crunch the numbers.” Each student came to this unit
with an investigative role and technique which has been developed within the group. This
teamwork promoted student-to-student interactions through cooperation in which the teacher
leads the discovery process with guiding questions from which an individual student’s answer
prompts another thought within the team, and so on, until conclusions can be drawn. The
students, when presented with a problem and the tools of investigation, assumed their roles
and worked to collect data as part of a team through experiments, then analyzed and
individually formulated conclusions based on their data. This was a technique with which the
students were very familiar, as they had learned through this method for their entire course

of physics.

Implementation of Unit

The goal of the sound unit was intended to facilitate an understanding of sound
motion, and ultimately, to cause students to appreciate the more complicated concepts of
superposition which create pleasing harmonies in music. “The foremost purpose of any
demonstration experiment is to clarify a physical principle or to show some interesting
application of that principle.” (Sutton, 193 8) A series of demonstrations and experiments
were developed to illustrate waves and sound during research done in the summer of 1997
and are listed sequentially as presented in Appendix A. The students experienced a
continuation of the firndamental wave properties first learned with the ripple tank experiments
and gained a greater clarity of these concepts. Extension exercises were also designed to
enhance student understanding of the concepts discovered or investigated in the experiments.

Students reported individually on their experiments by collecting the necessary data,
answering the questions provided with the experiments, and making conclusions based on the
data. Students were very familiar with this method of reporting. All prior physics units
required the same type of student summary. These reports were graded for the students but
were not considered part of the assessment for this thesis.

To paraphrase an old Broadway musical - we started at the very beginning. In the
instance of the sound unit, which required almost three fiill weeks of instruction, we began
with an experiment which investigated the speed of sound. The title of the experiment was,
appropriately, “Experiment #1 : Speed of Sound in Air.” After a brief discussion of
molecular involvement in the propagation of sound as compression waves, students were led

outdoors to the school’s athletic fields. Equipped with stopwatches, the students used their

reactions to determine the time between seeing the smoke from a starter’s pistol and hearing
the sound when fired at varying distances from the students. Students used their knowledge
of speed, acquired during an earlier unit on motion, to calculate speed of anything which
moves given the distances and the measured values for time. This experiment was found to
work fairly well at greater distances and combined classroom data provided an average value
near the expected 330 meters per second. Students had difliculty reacting accurately when
the stimuli of seeing the smoke and hearing the sound were close together in time. Student
reports were evaluated based on the ability to identify the speed of sound as constant.
Explanation of discrepancies from ideal data came fi'om classroom discussions and were to
be included in student reports.

A short demonstration activity was used to begin the next experiment. Students had
already been exposed to a standing wave on a Slinky" and in the ripple tank in the previous
unit. In addition, the concept of superposition had been introduced and discussed in the
preceding weeks. Another demonstration of the standing wave requires a piece of equipment
specifically designed to create a standing wave on a string by vibrating it at varying
frequencies. Since this device was not available, an economically prudent alternative was
devised during the summer research of 1997. This involved using a variable speed electric
drill spinning a metal coat hanger which had been cut and bent to hold one end of the string.

The other end of the string was fixed to the wall. When viewed from the side, students can
see a standing wave pattern. As they had observed standing waves in the ripple tanks before,
students could again see yet another example of a standing wave and identify its parts. Some

guided discussion during and following the demonstration showed an improvement in student

understanding of this presentation.

For the next experiment,
students used the standing wave
concept to understand resonance.
Some discussion led to the drawing
of a diagram similar to Figure 4,
showing students the standing
sound wave. Unfortunately, the
diagram may have contributed to
the misconception that sound waves
were transverse - despite discussion
specifically describing the

longitudinal nature of sound waves.

 

 

Transverse Wave Model

 

 

 

 

 

 

 

Air Pressure Model

 

 

Figure 4: Resonance occurs in a column of air by creating an
antinode at an open end. Represented here by the transverse
wave model (which students understand more easily) and the
more accurate longitudinal wave, due to air pressure difl‘erences.

Sound waves were then made to resonate in the tube with the equipment provided. The

length of the resonating air column, which was made variable by submerging it in water, was

then used to determine wavelength. This value was then used to find the speed of sound at

different temperatures. Students were instructed that resonance occurs when an antinode

vibrates at the mouth of an open-ended tube. A tuning fork - a simple way of creating a

constant, known fi'equency - was held at the open end of the tube creating the vibrations

necessary to make the wave “stand.”

Students performed the experiment “Experiment #2: Temperature and the Speed

of Sound” by producing resonance within a glass tube which was partially submerged in

10

notes. Unfortunately, students couldn’t see the waves in the glass tube, and - for some of
them - the experiment was “magic.” A worksheet titled “Resonance Worksheet #1 : The Air
Column" dealt with the mathematical relationships within a vibrating column of air and
supplemented the experiment. Student reports were graded based on their explanation of the
relationships between air column length, frequency, and wave speed, as well as descriptions
of the standing wave phenomenon.

Vibrating strings were used in the next experiment as the source of resonance. In
“Experiment #3: Vibrating Strings,” the students used a homemade sonometer that I
developed and tested for this thesis. The students placed a specified length of string under
a predetermined amount of tension. The vibration of this string was reproduced on another
string under varying tensions and lengths. The mathematical relationships between length and
tension of the string were graphed and determined. A few problems were faced with the
design of this experiment. Although students could see the string vibrate and see the nodes
and antinodes, it was difficult for many of them to think of this as a wave. Some students had
difficulty matching frequencies because the homemade sonometer was not hollow bodied and
therefore diflicult to hear. The force supplied to the strings by hanging masses was
quantified. However, due to a shortage of supplies, many students were required to wait for
other student groups, resulting in unnecessary time off the task. The direct relationship
between string length and the square root of the tension, which was derived graphically,
became one area of focus for these experimental results and student conclusions. Another
concept which was immediately obvious to the students dealt with the inverse relationship

between length of the vibrating string and its pitch. This is a relation very similar to one

11

developed in the previous unit where wavelength and frequency were inversely proportional.
Classroom discussion was utilized to help make these concepts understandable for all
students. Another worksheet creatively titled “Resonance Worksheet #2: The Vibrating
String” followed the experiment. The worksheet dealt with the mathematical relations of
a vibrating string and its tension, length, density, and pitch.

Musical notes, their related fiequencies, were presented to the students. The musical

scale was laid out as a number of frequencies which existed at whole number ratios with each

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

other (see
Figure 5)- A Diatonic CD IE F IG A B. 'C.
worksheet 1““ - . : 161.1 . i . i 161 -
Tempered 19.8 ,. 10.9 ,15 . 9.8 10.9 9.8 _ 15‘ f
titled “Music a _ . 7 .
Equally . 6-,. ,_ 6 1:: f _ 6 _ 6. _ 6 12
Tempered (2., ‘5 J5 J5 J2— fi fi
Worksheet #1: ~ -- -~ --~ ., .. . _.. _ ,_. _
The N ates,” Figure 5: Tone Intervals in the Just Scale and Equally Tempered Scale
emphasized

these ratios. Students then used knowledge of the scales and relative frequencies and
discussion to match fiequencies at the simplest whole number ratios to create harmonies.
Some classes had “brave” students who were willing to vocalize with each other in an attempt
to create harmonies. The simplest example students used was the octave, which has a two-to-
one frequency ratio, creating superposition with every other wavelength of one tone and
every wavelength of the other tone. Students were given a complete four octave scale with
frequency values to assist their investigations. Other ratios between 1: 1 and 2:1 were explored

and another worksheet, titled “Music Worksheet #2: The Harmonies and Chords,” was

12

 

completed.

A day of “playing” was the final investigative activity for the unit. Students who
owned musical instruments were encouraged to bring them to class. Using a homemade voice
amplifier (designed by me specifically for this thesis) and an oscilloscope, students were
encouraged to play around with the visual representation of each instrument - including their
voices. This was a very fi'ee-form day, as some classes had many participants, while others
did not. Class discussion was invaluable in the clarification of concepts which were brought
to the surface. Students brought only wind or stringed instruments representing the two types
of resonance studied in class.

Among the instruments were the comet and trumpet, which sounded the same to all
listeners in the class. These were shown on the oscilloscope at the same time using separate,
individual inputs. The difference in the trace was minimal, but students were able to see
overtones with the trumpet which were not present for the comet and vice versa. Several
students played in harmony in the same amplifier to produce complex traces on the
oscilloscope. “Beats” were produced using two guitar strings slightly out of tune with each
other. These visual representations of the “new” waves acted as a catalyst to revisit the
concept of superposition.

Upon completion of the unit, a review of major concepts and a test was given to
evaluate the students’ proficiency with the concepts presented in the unit. This “Sound and
Music Quiz” utilized multiple choice and computation to determine student understanding.
Another assessment was titled “Wave Assessment” and given specifically for this study to

determine students’ proficiency with the concepts of wave mechanics as a pretest and post-

13

test device. Although students had previously answered the same questions, for consistency
in this study, the responses were never identical.

This unit took approximately three weeks or fifteen class periods. Each of the three
experiments took at least one day for set up and a day for evaluation and discussion;
Experiment #3 required an additional half class. The four worksheets each took one class
period plus homework time. A demonstration activity required about a half class with
discussion. Preparation for the unit quiz and the quiz itself used two class periods. The pre-
test and post-tests for this thesis was also a single day event and the beginning and end of the

unit.

14

1.

fr: ‘1 en

 

Evaluation of Unit
Overview

The evaluation process of this unit for the purpose of this thesis was primarily through
a pretest and post-test, but other, more subjective, assessment techniques were also
implemented. The focus of the evaluative process was student understanding of concepts
relating to waves. There were no new instructional methods attempted, as the purpose of the
unit was to give students another set of phenomena fiom which to learn the concepts of wave
mechanics.

A pretest and post-test were given based on concepts related to waves which had
been taught prior to this sound waves unit. The assessment was in essay form, with no limits
given to length of response or time to respond. The concepts assessed were those that had
been identified as ones which, based on past performance on prior years’ examinations,
students lacked proficiency. The topics of the questions addressed included describing
mechanical energy transfer in the propagation of waves, comparing and contrasting transverse
and longitudinal waves, showing understanding of the relationship of wave speed, wavelength
and frequency, comparing and contrasting constructive and destructive interference, showing
understanding of standing waves, and explaining how one “feels” sound. These topics, while
not exclusively the goals of the waves unit, represented the bulk of the desired conceptual
base. Based on their responses to six questions, students were scored on a basic rubric of
four points per question (see Appendix B), in an attempt to keep the evaluation as objective
as possible. The rare score of four on an individual question showed complete proficiency

while a score of zero reflected a totally incorrect perception. The average student score for

15

f- 9- r‘mm.1
_ I
_

all questions on the pre-test was 25.61% (4.61 points earned out of a possible 18 points).
Later, after the unit was taught the same test was administered as a post-test; the average
score was 46.39% (8.35 out of 18). Because these are averages, these numbers didn’t
necessarily reflect the grth individual students experienced. The actual student data are
outlined in Table l, in Appendix C.
Quantitative Data

Each question was, as objectively as possible, evaluated using the assessment rubric
in Appendix B. These data are presented in histograms to demonstrate frequency of pretest
and post-test scores for comparison. For all test items the same one hundred five (n=105)
subjects were assessed. This large sample size was intended to increase the reliability of the
data. Some samples of student responses are also included for the more subjective
assessment. The names of these students have been changed to protect anonymity.
Question 1:

“How is mechanical energy transfer responsible for wave propagation? ” grading rubric:
O. No or totally incorrect response.

1. Vibrating air molecules bounce off one another.
Vibrating molecules of the medium of propagation collide causing a periodic wave to
form.

3. Energy is transferred by particles in the medium colliding in a periodic fashion. The

vibrating source moves the molecules of the medium immediately adjacent to it.
These molecules move the adjacent molecules and the energy is transferred until the
energy is “used up” or lost to external forces.

“Chad”, a senior male, answered Question One on the pre-test by saying, “Mechanical

energy will transfer from one object to another and that makes waves go forth (propagation).

In air, there are tiny magnetic fields around the molecules, so when the force comes and

16

pushes them together, they pass the energy on to keep their own space. That’s what
continues the wave along in any medium, the mechanical energy transfer.” In accordance
with the grading rubric, this response earned “Chad” two points on the pre-test. On the post-
test, “Chad” responded by saying, “Mechanical energy is basically the energy that allows work
to be done so it is mainly responsible for wave propagation because the energy that is
available in air molecules (mechanical) allows the wave to continue since the kinetic energy
(energy of motion) can be

transferred fi’om the molecules prior Q uestion 1 Scores

to the next molecules. The next Pre-Test I Post Test

‘1
O

molecules accept the energy of the

O)
O

molecules that hit them, and the

wave continues to go onward as

>4
0
C
0
3
5
IL

50
40
3O
20
1 O

0

long as some kinetic energy is left

(since the molecules have 2

Score

 

mechanical energy)” This response
Figure 6: Histogram of pretest and post-test scores for

earned “Chad” four points. Figure Question 1'

6 shows a histogram of scores earned on question number one. The total test group
improved their performance on this question by 0.632 points.
Question 2:

“Explain the dtflerence between transverse waves and longitudinal waves ” grading rubric:
O. No or totally incorrect response.

1. Transverse waves have amplitudes which are vertical and longitudinal waves have
amplitudes which are horizontal.
2. Transverse waves are like sine waves and have disturbances which are perpendicular

l7

to the direction of motion 0R longitudinal waves are compression waves which
vibrate in the direction of motion.

A transverse wave causes the particles of the medium to vibrate in a direction that is
perpendicular to the direction the wave is moving. A longitudinal wave causes the
particles of the medium to vibrate in a direction parallel with the direction of the
wave.

“Angela”, a senior female, earned two points on her pre-test by responding “A

transverse wave moves in an up and down motion. A longitudinal wave moves in a side to

side motion.” “Angela” responded

to the same question on the post-
test by saying “Transverse waves
move perpendicular to the direction
of motion, where as longitudinal
waves move parallel to the direction
of motion.” This response earned
“Angela” all of the possible points.
Figure 7 shows a histogram of Score

scores earned on question number

 

Question 2 Scores

Pro-test I Post-test

 

 

 

 

 

 

 

 

 

 

 

Figure 7: Histogram of Pre-test and Post-test Scores for
Question 2.

two. The total test group improved

their performance on this question by 0.688 points.

Question 3:

How does a wave ’s speed relate to its fiequency? Its wavelength? grading rubric:

0.

1.
2.
3

No or totally incorrect response.

v =fl..

Speed varies directly with frequency and wavelength.

With a constant wavelength, the wave’s speed is directly related to its frequency.
With a constant fi'equency, a wave’s speed is directly related to its wavelength. v =

18

fl.

“Misty”, a senior female, responded to this question this way “A wave’s speed is

proportional to its fi'equency and frequency times wavelength equals speed. So, if wavelength

or frequency increase, so will speed. However, if frequency or wavelength increases, the

opposite (fi'equency or wavelength) will decrease.” This earned “Misty” two points on the

pre—test. On the post-test, however she responded, “The faster a wave is going, the more

frequent it will be if wavelength is
constant. The bigger the
wavelength, the greater the speed if
frequency is constant. Frequency
times wavelength is speed.” This
response as outlined in the grading
rubric, of course, earned four points
for “Misty”. Figure 8 shows a
histogram of scores earned on

question number three. The total

 

 

Question 3 Scores

C] Pre—test I Post Test

 

 

 

 

 

 

 

 

 

50

40 "
§ 30 ‘a
. i
a r...

10 4 :x:

0 — “
O 1 2 3
Score

 

 

Figure 8: Histogram of Pro-test and Post-test Scores for
Question 3.

test group improved their performance on this question by 0.488 points - this was the least

change from the pre-test score in this study.

Question 4:

“Explain constructive and destructive interference. ” grading rubric
No or totally incorrect response.

1. Constructive interference is making big waves, destructive is making small or no
waves.
2. Constructive interference makes bigger waves, destructive interference makes no

19

waves because of superposition.

3. The principle of superposition allows for the adding of the displacement of individual
waves at a particular position in the medium to form one displacement. Constructive
interference occurs when the wave displacements are in the same direction,
destructive interference occurs when two waves -of equal displacement - overlap to
result in zero disturbance of the medium.

“Jeff”, a junior male, responded to the fourth question on the pre-test by saying,
“Constructive interference increases the velocity and frequency of a wave while decreasing
its wavelength. An example would be a wind blowing behind a wave. Destructive
interference decreases the velocity and fiequency while increasing its wavelength. An
example would be a wind blowing in fi’ont of a wave against its direction of motion.”
Obviously, “Jefl” had no idea what interference was and created his own definition using his
knowledge of the words constructive and destructive. He, of course, only earned one point
for this response. In all fairness to “Jeff’, and his many peers who responded similarly, very
little class time had been dedicated to studying wave interference prior to the sound unit.
After the sound unit, “J efl” responded to the same question this way, “Destructive
interference is the point on a wave where a node is formed. Constructive interference is the
point on a wave where an antinode is formed. An antinode is a point on the wave where a
crest or trough is formed. There is V2 of a wavelength between antinodes.” While “Jefl” did
not earn all of the points as outlined by the grading rubric, he did show a much firmer grasp
of the concept of interference, earning three points. Figure 9 shows a histogram of scores

earned on question number four. The total test group improved their performance on this

question by 0.664 points.

20

Question 5:

“How does a standing wave
‘stand? ”’ grading rubric:

O.

No or totally incorrect

response.
By creating nodes and
antinodes through

destructive and constructive
interference.

Reflecting a wave so that it
interferes with itself causes
nodes and antinodes.

A standing wave is the
result of identical waves
moving in opposite
directions. The reflection of
one periodic wave source is

 

 

Question 4 Scores

[:1 Pro-test I Post-test

 

 

 

8

 

0)
O

 

 

Frequency

 

 

N
O

 

 

 

 

Score

 

 

Figure 9: Histogram of Pre-test and Post-test Scores for
Question 4.

a possible method of producing standing waves. The areas of maximum displacement
- due to constructive interference - are called antinodes. The areas of total non-
disturbance - due to destructive interference - are called nodes.

“Charlie”, a senior male, remembered some of the definition of a standing wave in his

pre-test response to this question. “A standing wave stands when the incident and refracted

waves meet up due to high frequency and velocity making the waves hit each other over and

over quickly making the human eye see it as one wave when really it is many waves reflecting

back and forth.” This response was only worth one point. “Charlie” understood things a little

more clearly by the time he took his post-test and earned three points. “A standing wave

stands still when the crest and trough are lined up, making the wave look still at the same time

and a wave sequence such as: m ” Figure 10 shows a

histogram of scores earned on question number five. The total test group improved their

performance on this question by 0.648 points.

21

Question 6:

“Explain how you can feel’ the
music at a rock concert. ” grading

rubric:
0.

No or totally incorrect
response

They turn up the volume
causing the air to vibrate
around the audience.

High energy output of the
speakers vibrates the air
causing longitudinal waves.
The air around the audience
is constantly vibrated - the
skin detects this vibration
allowing the sound to be
“felt.”

 

 

Question 5 Scores

[:1 Pre-test I Post-test

 

 

 

 

.....

 

 

 

 

 

 

 

 

 

 

 

 

 

O
L
1.:

Score

 

 

Figure 10: Histogram of Pre-test and Post-test Scores for
Question 5.

The speakers vibrate the air molecules near them with massive amounts of energy.
This energy is transferred to adjacent molecules in a longitudinal wave to the
audience. The energy is so great that the air around the body is being violently
oscillated causing the skin to detect changing air pressure. Longer wavelengths (bass)
allow for more detection time between drastic pressure changes, therefore allowing
these to be the most “felt” sounds.

“Sara”, a senior female, had some thoughts about how you feel sound. Her pre-test

response was, “When one attends a rock concert he can feel the music because there is energy

being released from the instruments and coming out of the speakers. The energy is moving

through them, or vibrating through them. It does not go around them, some of it might, but

a little of it goes through them because a body can not block all of it out. Therefore, a person

is able to feel it because the energy is actually going through them.” “Sara” earned one point

on the pre-test. After the sound unit, “Sara” thought this about feeling sound, “I can feel the

music at a rock concert because the sound impulses vibrate out of the musical instruments,

and the frequency of the music carries through the air and does not stop when it comes in

22

contact with humans. Therefore, sound waves travel much like water waves in a rhythm-like
manner. Since the sound waves are traveling in a rhythm like motion they are then able to
permeate through most mediums including humans. Because of air molecules bouncing into
a human’s molecules the human feels the sound waves vibrate through him.” This response,
while still showing a connection with humans being a medium through which sound waves

travel, was worthy of three points

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

on the rubric scale. Figure 11 Question 6 Scores
shows a histogram of scores earned [:1 Pre—test I Post-test
on question number six. The total 50
40

test group improved their >.

g 30

0
performance on this question by §20

1:
0.736 points - this change 10
represented the greatest

 

 

Score

 

improvement by students in this

 

Figure 11: Histogam of Pre-test and Post-test Scores for

study. Question 6.

Qualitative Data

Some students didn’t improve their score as the above may indicate, because they
were already proficient. “Joe”, a senior male, answered the question about mechanical energy
transfer correctly on both tests. Pre-test: “The closest thing I can come to relating to this is
a hockey player hitting the boards. The player has energy. When he hits the boards, his
kinetic energy is transferred to them. This causes them to “wave.” The wave runs down the

boards away from the point of impact. I see each board like a molecule. When one is

23

disrupted, it bumps into its neighbor which hits its neighbor and so on. So transferring energy
to one point propagates it to the whole.” Post-test: “I guess you could say that a vibrating
string would have mechanical energy. As the string vibrates, it bumps against air molecules
on either side. So the string is doing work on the molecules. These disturbed molecules then
bump into other molecules creating a wave that moves out from the source, in this case the
string. That’s how mechanical energy can be responsible for wave propagation.” “Joe” used
different examples to illustrate his understanding of the concept. He did, however, use a
recent example of the vibrating string - an experiment in the unit - to explain his
understanding.

Other students weren’t proficient and didn’t improve on their scores. Some, in fact,
gave entirely different but still incorrect responses for both the pre and post-test. For
example, “Katy” - a senior female - answered the question about transverse and longitudinal
waves in two ways. Pre-test: “Longitudinal waves are straight. Transverse waves are curvy.”
Post-test: “Transverse waves are in the direction of motion. Longitudinal waves are
perpendicular to direction of motion.” “Katy” was incorrect on both tests, but on the right
track. When I questioned her responses in a later discussion she gave a more complete
answer. In an attempt to defend herself, she said, “I just didn’t want to write all of that down.
I thought (what I wrote) was enough.”

“Mike” is another example of students who did not improve. This senior male
originally thought of constructive and destructive interference this way: “Constructive
interference helps in the transmission of a wave. It adds to the wave. Whereas destructive

interference causes small breaks in the wave and makes transmission diflicult.” On his post-

24

test “Mike” said, “When listening to an AM radio we hear destructive interference quite often.
Destructive interference occurs when something blocks the transmission of the wave or there
is a break in that wave. Constructive interference on the other hand is something that adds
to the quality of the wave. It helps to make the transmission of the wave better.” “Mike” was
not alone in using a definition for constructive which means “to be helpfirl.” Students have
heard teachers tell them to “do something constructive and stop fooling around” for years.
The word destructive has also had a similar use, that led many students to think of destructive
interference as something which stops a wave’s motion. In discussions with some of the
students about this vocabulary mix-up, several responses showed that the students didn’t
know the vocabulary so used a learned contextual technique to “dissect” the word’s parts for
meaning.

Analysis of Data

The distribution of scores on the pre— and post-tests shows an improvement as well. As is
shown in Figure 12, the highest half of scores on the post-test was higher than the highest
quarter of scores on the pre-test. Not only were the range of scores larger in the post-test,

the mean and median scores

 

were increased as well. The

 

 

'— J 1i Pro-test

 

 

average score on the pre-

 

test was 4.63 points and on

 

 

I Pour-rm

 

 

the post-test 8.48 points.

 

 

The median score - the o 5 10 15 20

 

 

 

score which shows the Figure 12: “Box and Whiskers” plot showing the distribution of scores.
Each segment represents 25% of the scores.

25

middle of the distribution of scores - improved from 5 points to 8 points. All scores assigned

to student responses for both the pre-test and post-test are listed on Table 1 in Appendix C.

This improvement was
across the board. Only three of the
one-hundred-five showed a
decrease in score from pre-test to
post-test with an equal number
improving their scores by more than
four points, an equivalent of 22%
improvement. Figure 13 indicates
that over three quarters of the

subjects improved by up to seven

points on their total rubric score.

 

Change in Score

Poet-test minus Pro-test

  
 
 

El

/-"", f— 131
‘Vllgi :1

..
O

.5.
.s
N

11

1‘31

.
1,
51

l

 

 

 

Figure 13: Pie Chart Representing the Changes in Score. Each
Area Represents the Number of Students Whose Score Changed
by the Amount listed.

It was found through taking average pre-test and post-test scores, that students

improved their scores an average of 0.648 points out of three possible points or

approximately 22 percent. Table 2 shows average scores for test items. On the pre-test,

subjects scored an average below one point per item. On the post-test, students improved

their average score to nearly one and one half points.

26

Since female performance in

the “hard sciences” in general and

Table 2: Average Pre- and Post-test Scores for All Students

 

physics in particular is an issue of

 

discussion among many

 

 

pedagogues, I decided to look at

 

this issue using the results of this

 

study. Some analysis of data

 

 

separated into gender groups shows

 

Pre—test Post—test
. . . Change
Question pomts pornts .
m score
earned earned
1 0.657 1.314 0.657
2 0.771 1.467 0.696
3 1.248 1.733 0.485
4 0.619 1.295 0.676
5 0.524 1.162 0.638
6 0.762 1.495 0.733
Average 0.764 1.411 0.648

 

 

 

 

 

little deviation from the group as a

whole. A comparison of the sixty-

three males’ scores found an improvement average of 0.651 points or just over 21 percent.

The group of forty-two females averaged a little more than 20 percent improvement or 0.615

points out of the three possible. A
similar comparison of male and female
pre- and post-test data was also made.
As is apparent in Table 3 and Table 4,
there was a small difl‘erence in
performance between males and females
on the assessment. On the average pre-
test items, females were 0.233 points
lower than the males, the equivalent of

a 7.8% difference. On the post-test,

Table 3: Average Pre- and Post-test Scores for Female

 

 

 

 

 

 

 

 

Subjects
Pre-test Post-test

. . . Change

Question pornts pornts i r
earned earned n 500 e

1 0.690 1.167 0.477

2 0.786 1.500 0.714

3 1.095 1.714 0.619

4 0.429 0.905 0.476

5 0.190 0.810 0.620

6 0.619 1.405 0.786

Average 0.635 1.250 0.615

 

 

 

 

 

 

27

males averaged 0.269 points better than
females (9.0%). Interestingly, however,
both groups showed average increases
which difl'ered by only one percent. The
females improved more than the males
on three of the six questions. On the
other three questions, the males had a
greater improvement. Therefore,

contrary to many assertions, gender

differences do not affect student

Table 4: Average Pre- and Post-test Scores for Male

 

 

 

 

 

 

 

 

 

 

Subjects f
F Pro-test Post-test -
Question . oints . points
earned , earned , ;
1 0.698 1.397 0.699
2 0.778 1.444 ll 0.666
3 1.380 1.762 0.382
4 0.746 1.540 0.794
5 0.746 1.413 0.667
6 0.857 1.556 0.699
Average 0.868 1.519 ll 0.651 ‘

 

 

 

 

performance; at least within the scope of this study’s population and content.

28

Conclusion

Perhaps the most effective aspects of the sound unit (as with any unit) were the class
discussions which followed and supported the demonstrations, experiments and worksheets.
There was some predictability in the questions students asked and responses students gave,
but occasionally, a student epiphany would drive the discussion beyond its intended
boundaries. It was during the discussion periods that students’ understanding was evaluated
and clarified. Unfortunately, in class discussions, only the participating members can be
evaluated. All students who pay attention to the discussions, however, can benefit from the
discourse. The important thing for leading the discussions was to concentrate on topics to
which students could relate and maintain interest.

Many high school students are quite focused on music, as it is a major part of their
lives and is somewhat fascinating to the students. This fact supports the benefit in using
music in the discussions. Unfortunately, since discussion was the major way of promoting
understanding of the concepts, keeping the students’ interest wasn’t very simple. No practical
and affordable methods of showing students the relationships between fiequencies and
harmonies were found other than diagrams and calculations. There were no easy and tangible
tools to allow the students to conceptualize the alliance of music and physics. Perhaps, an
economically priced computer program, or musical keyboard would provide greater
opportunities for understanding these concepts.

It was also difficult to teach the physics of music to a group with varying levels of
musical background. Some students were well-versed in music theory, and brought a higher

level of understanding to the discussions. Others seemed happy to remember the order of

29

notes on a treble clef. The variety of backgrounds for this unit was much greater than for any
other unit in the course. The heterogeneity of this particular conceptual category was not a
problem, as few students had studied music in relationship to the fi'equency values and the
mathematics involved which helped close the gap. In addition, mathematics was a fairly
common experience for all students.

With any extended study, students tend to gain a greater understanding of the basic
concepts. \Vrth the sound unit, the purpose was for students to increase their understanding
of wave mechanics. An additional but less emphasized reason for teaching this unit was to
firrther expose students to the physics found in everyday events. This unit appears to have
proven efl’ective in its goals. The theory that “less is more” seems to be true here. Students
were not overwhelmed with many different concepts, they were exposed to a variety of events
dealing with waves which have varying degrees of complexity. It is this eclectic approach
which made the concepts understandable on difi‘erent levels by different students.

The data indicate that students indeed showed an improvement in demonstrating
understanding concepts demonstrated by the pre and post-test scores. Whether the
improvement was due specifically to the activities in the sound unit or would have occurred
merely with more time spent on experiments in the ripple tanks cannot be definitely
determined by the nature of the study. However, the first attempt at teaching this sound unit
was effective and will continue to be developed and taught.

With my experiences as a teacher in mind, I am very positive about this unit’s
effectiveness. The data support a conclusion that the unit was successful in its intended goal

of improving student understanding of selected fundamental concepts. Sometimes an

30

experiment or discussion just doesn’t seem to have the desired effect and sometimes a vast
majority of the students don’t see the connections that the activity is designed to demonstrate.
This unit had those moments, too. There were also the moments of epiphany and revelation
which drove the student understanding to a more complex level. It is these moments which
must be replicated for the unit to continue to be successful. Unfortunately, there is no real
recipe for these “ah-ha” moments. There is a magical mix of students, teachers, environment,
and discussion which makes the whole thing work. Given a different set of students, or a
different teacher, this unit may have been more or less successful. It is, however, undeniable
that the data supports the accomplishments of this unit, especially considering the relatively
large population of subjects used in this study.

In a holistic sense, there is no reason to believe that this unit doesn’t help students in
these concepts which are also central in the State of Michigan Department of Education’s
essential goals for science. In a very real way and on many levels, this unit was successfiil.
Not only did students show an improvement in conceptual understanding of topics to which
they had previously been exposed, but they also were exposed to different experiences

surrounding those ideas, thereby enriching their overall experience.

31

APPENDIX A

Experiments and Activities

32

Experiment #1 Speed of Sound in Air

Purpose: To use our senses to determine the speed of sound.

Theory: Light has a speed of about 3.0 x 108 m/s. Sound moves much more slowly.

We can see a distant event before we hear it. By timing the difference
between seeing and hearing an event and measuring our distance from the
event we can

determine the speed

of the sound.

Procedures:

1.

gargygzlgggeed , @illllllll»)lllll.

 

 

 

2. Stand on the opposite goal Stopwatch
line as your teacher. The
teacher will have a starter’s
pistol

3. When the teacher shoots .r
the pistol, start the
stopwatch when you see the
puff of smoke. Stop the
watch when you hear the
gun.

4. Record the time and repeat.

5. Double the distance
between students and teacher and repeat steps 3 and 4.

6. Record class data, calculate speeds, and class averages.
Remember: 1 inch = 2.54 cm.

Questions:

1. Approximately how fast does sound travel in air?

2. About how far away is a thunderstorm if you hear thunder 3 seconds afier seeing
the lightning (1 mi = 1.61 km)?

3. Why might the people at the end of a long marching band be out of step with the
front?

4. A spoken message fi'om the moon ((1 = 240,000 mi) can reach the earth in about
1.3 seconds. How is this possible?

5. Sound waves travel 4 times faster in water than air. When sound leaves air and

enters water, how are wavelength and frequency affected?

33

 

 

Standing Wave Demonstration

Theory: Standing waves are formed when a wave reflects on itself. The
superposition of the wave and its reflection create areas of constructive
interference known as antinodes. Areas of destructive interference are
known as nodes. When viewed from the side, a string being spun by an
electric drill appears as a standing wave.

 
 

3 meters of string ADChor

  
     

    

 

’\ Antinod::\’ i

 

  
 

 

Questions:

1. What is the relationship between wavelength and frequency?

2. How much distance, in terms of wavelengths, is between nodes? Antinodes?
3. How is a node created? How is an antinode created?

34

 

 

 

Experiment #2 Temperature and the Speed of Sound
Purpose: To measure the speed of sound of different frequencies in different
temperatures of air }
:7
Theory: A standing wave will occur when a we. m, a):
wave’s reflection interferes with its w. 09°- !“ 30}
incident path. The shortest column of air \“
that can have a node (destructive Ans-od- 11> g
interference) at the bottom and antinode W. i 3,
(constructive interference) at the top is <§ <§
1/4 A. Resonance will occur when a A-d-odo 3
tuning fork vibrates at the open end of a N“. : 5,
closed end tube in multiples of 1/4 A. \ (
Procedures: Mu“ <\) >
1. Place cylinders with hot water on one side of M \Y

 

 

 

 

 

the classroom and ice water on the other side of cm“ 3“
the classroom.
2. Record the value of the frequency that is stamped on the tuning fork.
3. Wear goggles while using tuning forks next to the glass tubes. Strike a tuning fork

to the palm of your hand.
4. Hold the tuning fork above the glass tube while you slowly raise the tube until the
sound is amplified and is loudest.

5. Measure 1, the distance from the water to the top of the tube, to the nearest .01 m.

6. Repeat steps 3 - 5 with the same fork but struck so that the tuning fork sound is
quiet.

7. Hold a thermometer in the middle of the glass tube and measure the air
temperature.

8. Trade places with another group on the other side of the room and repeat steps 3 -

7 using the same tuning fork.
9. Change the frequency and repeat.

Questions:

Are the values of “l ” different for loud and soft sounds?

How are the values for “l ” different for hot or cold air?

Write a general statement describing how the Speed of sound depends on loudness.

Write a general statement describing how the speed of sound depends on

frequency.

5. What would an orchestra sound like if the higher frequencies traveled at a difl’erent
rate than lower frequencies?

#5939!"

35

Resonance Worksheet #1 The Air Column

tube can also vibrate. When this occurs, the tube is said
to be resonating with the oscillating air pressure. The
reflection of the sound waves traveling through the tube
will interfere with the incident waves and cause standing
waves. In a standing wave, two nodes (or antinodes) are
separated by V22.

(fundamental) resonant length or harmonic is V41, the
second resonant length is 3A)., and so on in odd multiples
of V4. When the tube has an open end, the tube resonates
with the vibrating air at V2). (firndamental), 1)., and so on c...“ 2.4

When the air inside a tube is made to vibrate, the

gill

Open and

 

When the tube has a closed end, the first

 

 

xi *3
/ \

Open End

 

 

 

 

in even multiples of V211.

PLACE THE CORRECT RESPONSE IN THE SPACE BELOW EACH PROBLEM. SHOW WORK ON
ATTACHED SHEET OF PAPER.

1.

A tuning fork with a frequency of 400 Hz causes resonance in a 20°C air column
which is 43.0 cm long. What is the speed of sound in that temperature air?

A sound wave in a fluid medium (water) is reflected at a barrier so that a standing
wave is forced. The distance between nodes is 3.8 cm and the speed of propagation
is 1500 m/s. Find the frequency.

Determine the length of an open organ pipe that emits middle C (262 Hz) when the
temperature is 20°C (see question #1).

A flute is designed to play middle C (262 Hz) as the fundamental frequency when all
the holes are covered. Approximately how long should the distance be from
mouthpiece to the far end of the flute (v = 343 m/s)?

How far from the end of the flute (from question #4) should the hole that must be
uncovered to play D above middle C (294 Hz)?

The speed of sound changes 0.60 m/s per degree centigrade - colder is slower. What
frequency will be sounded if a flutist attempts to play middle C in 10°C weather
without “warming up” her flute?

A pipe has a length of 2.46 m. Determine the frequencies of the first three harmonics
if the pipe is open at each end. Let 335 m/s be the speed of sound in air.

What is the lowest possible frequency if the pipe from question #7 is closed at one
end?

36

Experiment #3 Vibrating Strings

Purpose: To see how tension and length afi‘ect the frequency of a vibrating string

Theory: When drawn tight with some constant force (tension), a length of string will

only vibrate at a specific fimdamental frequency. A guitar player will change
the length of the vibrating strings by pressing them at various ridges (called
frets) which lie beneath the strings. S/He can also adjust the pitch of a string
by changing the tension to get it “in tune.”

Procedures:

1.

 

 

Cut 1.5 m of l— l I
high test fish
line. Tie
s t r i n g
through hole
in peg #1.
Make a loop
at the free '

end of the F = mg (g
string.
Repeat for peg #2 and clamp the board to the lab bench with the other end hanging
over the edge.

 

 

 

 

 

 

 

®®

 

 

 

 

 

3. Hang 25 N from line #1, adjust the fret to a length of 1.0 m.

4. On line #2, hang 20, 15, 10, and 5 N. Adjust the fret length to produce an equal pitch
as line #1 - use your ear to make this as accurate as possible.

5. Graph length (I) vs tension (F).

Questions:

1. Does pitch increase or decrease when the vibrating string’s length is increased.

2. How does pitch change with increased tension?

3. What is the specific relation between I and F?

4 Frequency is indirectly proportional to string length and directly proportional to the
square of its tension. How must the tensions compare if string two has twice the
length of string one in order to maintain equal pitch? Try it to be sure.

5. How much tension must a 1.5 m piano wire (m = 0.0005 kg/m) have to produce the

standard pitch A“0 (f = (21)“(F/m)” )?

37

Resonance Worksheet #2 The Vibrating String

A

If stretched string is fixed at both ends, 1 mama“ 2A
waves travelling along the string will reflect at these //77

fixed ends causing waves travelling in both directions. These “
waves will interfere with each other causing standing waves. \
Points of destructive interference are nodes and are 2nd mmmfi _//\
stationary, points of constructive interference are v/ /
antinodes and move at a maximized amplitude. \v

The fundamental fiequency (first harmonic) [\\/\\/\
for a string is a function of rts length L, mass per 3“: mmonk/
unit length (density) 11, and the tension F on the \/\/\ p/
string.The subsequent harmonics are found to be multiples of
this firndamental frequency

v F 1 F
. :_ ; 21:). ; _: :_ _
f1 \J: f mi:

PLACE ma connecr RESPONSE in nu; SPACE BELOW EACH PROBLEM. Snow WORK ON ATTACHED sneer or PAPER.

1. The G string on a violin has fundamental frequency of 196 Hz. The length of the
vibrating portion is 32 cm and has a mass of 0.55 g. Under what tension must the
string be placed?

 

 

 

2. An unfingered guitar string is 0.70 m long and is tuned to play E above middle C (330
Hz). How far from the end of the string must the finger be placed to play A above
middle C (440 Hz)?

3. Find the speed of waves on a 0.80 g violin string 22 cm long if the frequency of the
firndamental is 920 Hz? What is the tension on the string?

4. Ifa cello string is tuned to a certain note, by how much must the tension be increased
if it is to emit a note of double the original frequency (1 octave higher)?

5. A certain violin string is 30 cm long between its fixed ends and has a mass of 2.0 g.
The string sounds an A note (440 Hz) when played without fingering. Where must
one put one’s finger to play a C (528 Hz)?

6. The highest key on a piano corresponds to a frequency about 150 times that of the
lowest key. Ifthe string for the highest note is 5.0 cm long, how long would the
string for the lowest note need to be if it were the same mass per unit length and
under the same tension?

7. Find the first four harmonics of a string 1.0 m long if the string has a mass per unit
length of 2 x 10‘3 kg/m and is under a tension of 80 N.

38

 

Music Worksheet #1 The Notes

The Musical Scale is based on fiequencies. An “C. E: * g, g: Q: g; D' .
octave is the progression through one whole range of ‘ '

 

 

 

 

 

 

 

 

 

 

 

 

 

notes so that the frequency is doubled. For example, in
the diagram at the right the “C” which is farthest left
will give a frequency of 264 Hz and the “C” which is C D E F G A B C D

 

 

 

 

 

 

 

 

 

 

 

 

closest to it on the right will be at 528 Hz. Octaves are

usually measured from “C” to “C.” The standard reference pitch, or frequency, is an “A” note
with a frequency of 440 Hz. This standard pitch is often called “A” above middle “C.”
Middle “C” has a frequency of 264 Hz. From middle “C” the next highest non-sharp/flat note
frequency is 9/8 times as large, next is 5/4, then 4/3, 3/2, 5/3, 15/8 and 2/1 will end at the next
“C” note (all multiples of the original 264 Hz).

 

 

 

 

1. Based on the previous statement, completely fill in the rest of this table:

’ Scale Note C D E F G A B C
Scale Ratio * 1/1 2/1
Frequency (Hz) 264 440
Voice Note Do Re Mi Fa 80 La Ti Do

 

 

 

 

 

 

 

 

 

 

 

2. What note would have a fiequency of 220 Hz?

3. What is the frequency difference between F and G in the middle octave (see above)?

Since there are some frequencies between the whole step notes, we use what are
called sharps and flats. A sharp for a note has a frequency which is higher than its own, and
a flat was a frequency which is lower. For example, a “C” (said “C-sharp”) will have a
frequency between the “C” and the “D.” There are two difl‘erent scales for dealing with
sharps and flats. The chromatic scale says that each sharp is 25/24 times the frequency of its
note, and the flat is 24/25 times that note’s frequency. The equal tempered scale uses 440
Hz as the standard pitch and divides the octave into 12 equal ratio intervals with each
semitone being 1.0594 times the frequency of its previous note. In the equal tempered scale,
a “C”” and a “D"” are the same note.

4. On the chromatic scale, what is the frequency for “F”” above middle “C” and what is
“G"” in that octave?
5. Answer question #4 for the equal tempered scale.

39

Musical Scale for 4 Octaves f _ . A

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. A Note Freq. (Hz) j , Note Freq. (Hz)
C 132.0 C 528.0
Ctl/Db 140.0 Cit/Db 560.0
D 148.5 D 594.0
DrI/Eb 140.3 Dit/Eb 561.0
B 165.0 B 660.0
F 176.0 F 704.0
Flt/G12 187.0 Fti/Gb 748.0
G 198.0 G 792.0
Gil/Ab 209.0 Gil/Ab 836.0
A 220.0 A 880.0
Art/Bl; 233.8 Ati/Bb 935.0
B 247.5 B 990.0
C 264.0 C 1,056.0
Cit/Db 280.5 Cit/Db 1,122.0
D 297.0 D 1,188.0
Dti/Eb 313.5 i Dti/Eb 1,254.0
B 330.0 l E 1,320.0
F 352.0 F 1,408.0
Ftl/Gb 374.0 Fri/G1: 1,496.0
G 396.0 G 1,584.0
Git/Ab 418.0 Gil/Ab 1,672.0
A 440.0 A 1,760.0
Ari/Bl) 467.5 Ail/B12 1,870.0
B 495.0 B 1,980.0

 

40

 

 

Music Worksheet #2 The Harmonies and chords

Harmony occurs when two or more frequencies
sound pleasing together. This occurs when the
frequencies exist in a small whole number ratio. The
smaller the whole numbers giving the ratio between
frequencies of the two notes the more harmonious is the

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

resultant. These are so important to music that each

ratio has been given a name. Here the frequency ratios are listed in decreasing harmony:
2:1 is an octave, 2:3 is a fifth, 3:4 is a fourth, 4:5 is a major third, 5:6 is a minor third,
3:5 is a major sixth, and 5:8 is a minor sixth.

1. If these harmonies are sensed due to superposition of the waves, draw a picture
representing the wave overlap (interference) created with an octave harmony.

2. Name the frequency which would make a fourth with 440 Hz.

3. What note will make a major third with “B” above middle “C” (495 Hz)?

4. What name would you give the harmony of “F” and “8"?”

Triads or chords are formed by 3 separate notes. Each note must be harmonious with
the other two while the highest and lowest notes are less than an octave apart. There are only
six ofthese, their frequency ratios are: 4:5 5:6, 3:4 4:5, 5:6 4:5, 5:6 3:4, 4:5 3:4, and 3:4 5:6.
5. What ratios exist in a chord with a major third followed by a minor third?

6. If the chord from question 4 has 264 Hz as its lowest frequency, what are the
frequencies for the other two notes?

7. What ratios exist between “F,” “A,” and “C?”

8. A chord called “A minor” has “A” as it’s middle note and frequency ratios of a fourth
followed by a 5/8 ratio. What are the three notes and their fi'equencies for this triad?

41

Sound and Music Quiz
Multiple Choice: 2 points each. Circle the letter of the best answer.

1. As a steel strip vibrates fiom left to right, it:
a) does work on gas molecules on the right,
b) transfers energy from the gas molecules on the right,
c) does work on the gas molecules on the left side,
d) transfers energy to the gas molecules on the left side.
2. Sound waves are:

a) longitudinal waves in space b) longitudinal waves in matter

c) transverse waves in space d) transverse waves in matter
3. Sound travels at a speed which is:

a) faster than light b) the same as light

c) slower than light (1) 200 m/s at 100°C
4. The speed of sound in air:

a) decreases with a rise in temperature b) is constant

c) increases at 0.6 m/s per °C d) is about 200 m/s at 100°C

5. Resonance is:
a) the vibration of air molecules
b) a frequency of vibrating glass
c) two or more substances vibrating at the same frequency
d) the length of an air column vibrating with water below
6. The slide on a trombone changes:
a) the pressure of the vibrating air column
b) the length of the vibrating air column
c) the temperature of the vibrating air
(1) the intensity of the vibrating air
7. A string of a certain density will vibrate:
a) twice as fast with twice the tension
b) half as frequent with twice the tension
c) twice as fast with quadruple the tension
(1) half as frequent with quadruple the tension
8. Harmonics are:
a) multiples of the fundamental frequency
b) the difference between two fiequencies
c) frequencies which occur in whole number ratios greater than V2 with each other
(1) sympathetic vibrations caused by an oscilloscope
9. Some pairs of tones sounded together are pleasing; these tones:
a) are harmonious
b) are discordant
c) may have fi'equencies between 10 and 50 Hz
(1) may have frequencies which differ by 68 Hz

42

Questions/Problems:
10.

.At room temperature

 

What range of vibrations
(frequencies) can most
humans hear? (2 points)

 

 

 

 

(20°C) sound travels at 342
m/s.Whatrangeof CDEFGABCDE

 

 

 

 

 

 

 

 

 

 

 

 

wavelengths can humans

. :.8:9 9:1015216 8:9 9:10 8:9 15:16 8:9
hear? (3 pornts) Tm‘e mm

. The equal tempered scale uses A (440 Hz) as the standard pitch and an octave is divided

into 12 equal ratio intervals. If A above middle C is 440 Hz, what is D” above middle
C? (5 points)

. The chromatic scale uses A (440 Hz) as the standard pitch and each sharp (”) or flat (b)

fi'equency is in a 25:24 ratio of its primary note. Find D” above middle C and E" above
nridle C. (6 points)

. A bass guitar string is 90 cm long and is tuned to A(110 Hz). To what length must it

be “fingered” in order to produce B in the same octave? (6 points)

. An open vertical tube is filled with water and a tuning fork vibrates over its mouth. As

the water level is lowered in the tube, resonance is heard when the water level has
dropped 17 cm and again afier 51 cm of distance exists from the top of the tube to the
mouth of the tube the temperature is 20°C. What is the frequency of the tuning fork? (3
points)

. A slide whistle has a length of 27 cm. Ifyou want to play a note one octave higher, how

long should the whistle be if the temperature is 20°C? (3 points)

. One open organ pipe has a length of 810 mm. A second pipe should have a pitch one

major third higher (frequency ratio of 4:5). How long should this pipe be at 20°C? (4
points)

43

APPENDIX B

Assessment Rubric

44

Waves Assessment grading rubrics

How is mechanical energy transfer responsible for wave propogation?

0. No or totally incorrect response.

1. Vibrating air molecules bounce off one another.

2. Vibrating molecules of the medium of propogation collide causing a periodic wave
to form.

3. Energy is transfered by particles in the medium colliding in a periodic fashion. The

vibrating source moves the molecules of the medium immediately adjacent to it.
These molecules move the adjacent molecules and the energy is transfered until the
energy is “used up” or lost to external forces.

Explain the difference between transverse waves and longitudinal waves.

0. No or totally incorrect response.

1. Transverse waves have amplitudes which are vertical and longitudinal waves have
amplitudes which are horizontal.

2. Transverse waves are like sine waves and have disturbances which are

perpendicular to the direction of motion 0R longitudinal waves are compression
waves which vibrate in the direction of motion.

3. A transverse wave causes the particles of the medium to vibrate in a direction that
is perpendicular to the direction the wave is moving. A longitudinal wave causes
the particles of the medium to vibrate in a direction parallel with the direction of
the wave.

How does a wave’s speed relate to its frequency? Its wavelength?

0. No or totally incorrect response.

1. v =fl..

2. Speed varies directly with frequency and wavelength.

3. With a constant wavelength, the wave’s speed is directly related to its frequency.

With a constant frequency, a wave’s speed is directly related to its wavelength. v =

n.

Explain constructive and destructive interference.

0. No or totally incorrect response.

1. Constructive interference is making big waves, destructive is making small or no
waves.

2. Constructive interference makes bigger waves, destructive interference makes no
waves because of superposition.

3. The principle of superposition allows for the adding of the displacement of

individual waves at a particular position in the medium to form one displacement.
Constructive interference occurs when the wave displacements are in the same
direction, destructive interference occurs when two waves -of equal displacement-
overlap to result in zero disturbance of the medium.

45

 

How does a standing wave “stand?”

0

1.
2.
3.

No or totally incorrect response.

By creating nodes and antinodes through destructive and constructive interference.
Reflecting a wave so that it interferes with itself causes nodes and antinodes.

A standing wave is the result of identical waves moving in opposite directions.
The reflection of one periodic wave source is a possible method of producing
standing waves. The areas of maximum displacement - due to constructive
interference - are called antinodes. The areas of total non-disturbance - due to
destructive interference - are called nodes.

Explain how you can “feel” the music at a rock concert.

0.
1.
2.

No or totally incorrect response

They turn up the volume causing the air to vibrate around the audience.

High energy output of the speakers vibrates the air causing longitudinal waves.
The air around the audience is constantly vibrated - the skin detects this vibration
allowing the sound to be “felt.”

The speakers vibrate the air molecules near them with massive amounts of energy.
This energy is transfered to adjacent molecules in a longitudinal wave to the
audience. The energy is so great that the air around the body is being violently
oscillated causing the skin to detect changing air pressure. Longer wavelengths
(bass) allow for more detection time between drastic pressure changes, therefore
allowing these to be the most “felt” sounds.

46

APPENDIX C

Student Data

47

Table 1: All data gathered from pre-test and post-test

‘ [ ,‘FOSt'tCSt Scores 3

. Preetest Scores

 

.1 a,"

 

18W ”

 

‘15.:

. 13»:

13

13

13

l4

14

15:

‘13  

'14

11

 

 

 

 

 

 

Ii

 

 

 

 

 

 

2

0

3

0

 

3

0

3

3

2

0

2

1

0

0

l

l

l

0

l

0

0

0

2

0

0

l

0

0

0

0

 

5 03001

 

a 03020-4
04005
'oams'

 

 

 

0800731.}

 

 

1 08010 }

 

"1 08027

 

; 0803-2 T

 

1 08043 7

5-16005§
. 16007 5

 

 

 

V 16020 ';

 

16039,;

 

16040

7116042 ?

 

 

1.16048'5

 

’ 16073 5

 

16103_j

L

 

19439 i‘
19452
.9..."
I, 19505

 

 

 

 

r9512C
i ‘19637H5

 

 

1,196581
351296.62

 

 

 

48

Table 1: Continued

7 .A,; ,.-

tremetss,,,  ;,

 

 

smell 1

 

g 1
1m

in

11

13

14"

n

11

10 p

10

11

12

16

13

11

 

 

 

 

 

 

 

 

 

 

 

 

2

0

0

 

l

0

2

2

0

0

0

l

0

0

0

0

0

l

0

l

l

0

3

0

0

3

0

1

0

l

 

 

i1,9672:

 

19673'5

 

19674 F

 

19°86.f

‘»39°9l .

 

 

.19702‘;

 

19716.

 

19719:

1.

 

I 19724.?

 

5’19723f

 

19731 > .g

 

I 19757,:

 

l9758i

 

19770 ;

 

'FH19771‘2

l

 

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19777 ii:

 

‘i.l9782 :

 

”119783'h

 

3198.45 ;

 

% «19.8697

 

‘.2mn2

 

L 20076 j
20127

 

 

120140,;
9 204146.,

 

5,20232;'

 

 

 

49

. _ Post-testScores .

Table 1: Continued

. Pre-test Scores 1

 

:TSnuksnl

 

 

10

10

‘15

10

11

_12

12

 

 

 

 

 

 

 

ll“

 

 

 

 

 

2

0

 

l

3

l

l

0

O
0

l

0

0

0

0
2
2

l

0

0
0

l

2

0
0
0

2

O
0

 

 

'_ 20268

: 20650 ‘1

 

 

721184 
' 21433

 

21575
21592

 

 

 

921646

21792 ‘

 

22149
22337

 

 

22456
22509
‘;22512 f
22513
22654

 

 

 

 

 

' , 22689

 

23339

3 26008

 

 

$.22728

 

 

(26009

J 26042

 

 

 

 

j:26063
‘ 27066
a 37010
.37015

37021
37026

 

 

 

 

50

Table 1: Continued

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6 5 4. mm 3 6.8.. 7 6 7mm. 9. 9
w. 0 2 l 2 2 l 2 l 2 0 0 2 0 2 0 2 0 U
.S.
a... 3
.w 0 O O 3 0 0 1 O O 0 2 0 2 0 2 3 3 .L
..
n...
.o. 8
.P. l l 0 0 0 2 3 2 2 2 2 2 2 l O 3 2 L
. 5
. 3 l 2 3 0 l 2 0 1 2 3 2 2 1 l 2 2 l.
.M 3
O 0 0 l 0 l 3 2 0 l l l 2 0 0 3 l .L
. 4
9
m 0 0 l 2 0 0 2 O O 0 l 0 0 l 0 2 O M.
w, 0 0 0 3 0 0 0 0 0 2 1 0 2 0 O 3 0 M
t
—
P. l O 0 2 0 O 2 0 O 0 1 l 2 l 0 3 l U
0 l 0 0 0 0 2 0 0 0 l 1 l 2 0 0 0
. 0 0 0 0 l 0 3 2 1 O 0 0 0 0 l 3 0
m “9...... 233m emanwe 2.463
. , O. 0.0 1...] 1.1.1 .2 2.2.1....1. W Wrouo
41122.2,333.3.3 4.52 4.4
S.. (7 8.8 8,8 8 8 8.8 8.8.8 8 9 9.999

 

 

 

51

REFERENCES

52

REFERENCES

Adamovic, Charles, and Hedden, Carol J ., “Problem-Solving Skills” HEW,
September, 1997. pp 20-23

Blackwood, O. H., Herron, W. B., and Kelly, W. C., Highjchoolflhysics Ginn and
Company, New York, 1961.

Dull, C. E., Metcalfe, H. C., and Williams, J. E., Physicsflqubggk, Holt, Rinehart and
Winston, Inc., New Yorlg 1964.

Grambs, Jean D.. and Carr. John 0, ModernMethodsinjemndanLEducationfifih
edition. Holt, Rinehart and Winston, Inc., New York, 1991. ISBN 0-03 -030408-3

Halliday. D. and Resneck R., Wormwood John
Wiley & Sons, New York, 1988. ISBN 0-471-81995-6

Michigan State Board of Education, WWW
EducationinZl 1991

Ostdiek, V. J ., Bord, D. J ., WW, West Publishing Company, New York,
1987. ISBN 0-314-93402-2

Penick, John, et a ., “Questions are the Answer” W, January 1996. pp
27-29.

Satumelli,A.M. .H'i-. 1‘515“‘0'0'411 '.-.1' 10
Charles E. Merrill Publishing Co., Columbus, Ohio, 1981. ISBN 0- 675- 02822-1

Sears, Francis W., Zemansky, Mark W., Young, Hugh D., W fifth edition,
Addison-Wesley Publishing Co., Reading, Massachusetts, 1980

Serway, R. A., and Faughn, J. S., Wu, Harcourt Brace College
Publishers, New York, 1992. ISBN 0-03-076377-0

Smithenry, Dennis, and Bolos, Joan, “Creating a Scientific Community” messaging
Teacher, November 1997. pp 44-47.

Snedden, David, WW1], Houghton Mifflin, Chicago, 1917.

Sutton. Richard M, DemonstratianExnerimentainPhxsies McGraW-Hill. New York.
1938.

53

Van Bergeijk, Willem A., et 81, W, Anchor Books Doubleday &
Company, Inc. Garden City, New York, 1960.

Washton. Nathan 3. WWW Harper & Brothers
Publishing, New York, 1961

White. H. 13.. ClassicaljniMQdemfihxsies 1940-

Zitzewitz, P. W., and Murphy, J. T., W, Merrill Publishing
Company, Columbus, Ohio, 1990. ISBN 0-675-02473-0

54

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