Lesson: Musical Instrument (Application Exp.)
1. NJ standards addressed in the lesson:
5.2.12.E.2: Objects undergo different kinds of motion (translational, rotational,
and vibrational).
Content-wise, the project deals with using vibrations of a string (or tube) to create sound.
Frequency, and therefore pitch, can be used be altered by changing tension, length, or mass
density (size string).
5.1.12.B.3: Revise predictions and explanations using evidence, and connect
explanations/arguments to established scientific knowledge, models, and
theories.
AND
5.1.12.C.1: Reflect on and revise understandings as new evidence emerges.
AND
5.1.12.C.2: Use data representations and new models to revise predictions and
explanations.
AND
5.1.12.C.3: Consider alternative theories to interpret and evaluate evidence-based
arguments.
The instruments will be built with the idea of the speed of waves in a string and how this
effects the frequency of the wave (and therefore vibrations). Since all the equations
involved are under ideal situations, not all calculations made will be precise and give the
expected frequencies. Students will have to reason through these inconsistencies.
5.1.12.D.1: Engage in multiple forms of discussion in order to process, make sense
of, and learn from others’ ideas, observations, and experiences.
AND
8.1.12.C.1: Develop an innovative solution to a complex, local or global problem or
issue in collaboration with peers and experts, and present ideas for feedback in an
online community.
Students will work together in groups (if possible containing individuals of various
strengths and backgrounds) to collectively solve the problem at hand and each contribute
their own knowledge and ability.
2. What students should know before they start the lesson:


Tension
Oscillations and waves:
o Relationship between frequency and:
 Tension
 Linear Mass density


 Wave velocity
 Wavelength
Resonance
Engineering and design process
3. Goals of the lesson
Content:
Goals
Oscillations and waves
Standards Addressed
5.2.12.E.2
Process:
Goals
Standards Addressed
Understand parts of the Engineering Design Process
8.1.12.C.1, 5.1.12.D.2
Conduct an application experiment
5.1.12.C.1, 5.1.12.C.3
Systematically make small changes when problems arise
5.1.12.C.3
Epistemological:
Goals
Standards Addressed
Understand why a given solution does not work and come up
with solutions.
5.2.12.E.2, 5.1.12.C.1,
5.1.12.C.3
Analyze what assumptions were made and how they affect
results
5.2.12.E.2, 5.1.12.C.1,
5.1.12.C.3
Learn to appreciate and use others’ abilities and cooperate to
achieve a common goal
5.1.12.D.1, 8.1.12.C.1
Learn the difference between engineering and physics.
5.2.12.E.2, 5.1.12.D.1,
8.1.12.C.1
Metacognitive:
Goals
How can I contribute my strengths to the discussion and help
solve the problem?
Standards Addressed
5.1.12.D.1, 8.1.12.C.1
4. Most important ideas



Aspects of the engineering process: Identify the problem, research the problem (mathematical
approach), develop possible solution, construct prototype, test and evaluate,
Redesign/communicate solution.
Evaluating assumptions and application of theory is not always straight forward.
Addressing problems with design one at a time, not all together


The practical difference between engineering and physics
How sound is created and what allows an instrument to make different sounds
(notes/pitches/frequencies)
5. Student potential difficulties:

Understanding why outcome did not match predicted values from mathematical
calculations.
 In the case of a stringed instrument, the frequency that sounds when a string is plucked
has to do with the tension on the string and the linear mass density. However, this is
under the assumption that the string cannot stretch. This will change the resulting
frequency slightly. So when a student plucks a string and finds that the frequency does not
match their prediction, students need to be reminded of their assumptions and the
assumptions taken by the equation they are using in their calculation.

Why the instrument is not loud enough to hear.
 If students are unfamiliar with other stringed instruments (guitars, violins, etc) then they
may not be familiar with the resonance chamber, a box with empty space that allows the
sound to resonate and be heard. Although this instrument need not include one of these
chambers, in the follow-up questions, students will be given an opportunity to give ideas
for how to improve their design. Here students may include Ideas to make the instrument
louder.

The actual construction and design process.
 Students need to be reminded of the type of difficulties actual engineers have with
construction. Sometimes designs need to be reevaluated if the initial design does not work
out as planned and sacrifices may have to be made in design or construction in order to
achieve something similar to the original design.
ex:
“What is standing in the way of you succeeding with your original design?”
“Rather than having each string make only one note, is there a way to make one string
make several notes?”
6. Equipment needed:
Student Use
 Wood Pieces
 Eye screws
 Wood screws
 Hinges
 Guitar strings
 Wooden Dowel
 Ruler
Teacher use
 FFT scope software
(http://duncan.rutgers.edu/physicsfreewares.htm)
7. Lesson description:
Musical Instrument Design(Application Experiment)
Lab Goals:
 Be cautious of assumptions
 Learn to redesign without trial and error
 Apply knowledge established in class to achieve a real goal
 Understand the process behind making music
The story:
A music company has come to you for a design for a cheap new instrument so that students
who cannot afford expensive fancy guitars and violins can still learn and experience music.
However, they have come to you in very short notice, so you don’t have time to go out and get
materials.
All you have are the following materials:
Building materials:






A piece of wood (24 in.×2 in. ×2 in.)
A few Eye screws
A few wood screws
A small hinge
A guitar string
Some wooden dowels
Measuring materials:




Spring scale
Measuring tape
Mass Scale
Computer with FFT Scope
Design Parameters:
The music company has requested that the instrument:
 Be as cheap as possible to make
 It needs to make at least 2 different notes (three different, distinct frequencies)
 That it cover a one octave range
o fhighest note =2× flowest note
 It does not have to be loud, but it does need to make an audible sound.
 The music company has agreed that the better the instrument, the more they are willing to
excuse the price:
o 2 distinct notes: Full price
o 3-5 distinct notes: 5% of final price excused
o 6-12 distinct notes: 10% of final price excused
o Over 12 distinct notes: 25% of final price excused
Procedure: Follow the steps below and fill in the proper sections in the Engineering/Design
Process handout.
a) To see what kind of frequencies make what kind of notes, use the Function generator in the
FFT scope software to play sounds at different frequencies (choose Function generator→
Sine) to start playing a tone. Press F9 to enter in a frequency you wish to hear.
b) Once you choose a frequency you would like to try to recreate, use mathematical
calculations with the materials you have to see if it is achievable.
c) Once you have a goal and have calculated the parameters of your instrument, plan how you
will build it. Make sure to include drawing with specific measurements.
d) Use the materials list to keep track of your cost.
e) Start constructing your instrument using the materials you “purchased” above.
f) Note any problems you come across in the building process. How did you overcome them?
g) Use the FFT scope to see how many different notes (frequencies) your instrument can
make.
Number of Frequencies:_________________
h) What is your final design? How is it different from your original design?
i) Find your final Price.
Step
1) Problem: What
kind of instrument
do you want to
build?
2) Research: What
freq. will you aim
for? Do all
mathematical
calculations needed
to find parameters
to achieve this.
Design Process Handout
Notes
3) Possible Soln’s:
Draw designs and
specific
measurements for
your instrument
4) Best Possible Soln:
Sketch final design
and what/how
many materials you
need.
Material
Wood
Eye screws
Wood screws
Hinge
Dowel
Guitar string
5) Soln. design
features: Describe
design features.
(How do you play
the instrument?
How many notes
can it play? Etc)
Cost Per Unit
$3
$0.15 each
$0.10 each
$0.75 each
$0.05 per inch
$1.00 each
Amount
1(only)
_______× $0.15 =
_______× $0.10 =
_______× $0.75 =
_______in × $0.05 =
_______× $1.00 =
Initial Total Cost=
Total:
$3
$_________
$_________
$_________
$_________
$_________
$
6) Construct, test,
and evaluate: Start
building your
instrument. Note
any changes you
made during
building.
7) Communicate
Solution: If your
original design did
not work, explain
why.
8) Redesign: Draw
your final
instrument. How
many notes can it
play?
Material
Cost Per Unit
Amount
Total:
1(only)
$3
Wood
$3
Eye screws
$0.15 each
_______× $0.15 =
$_________
Wood screws
$0.10 each
_______× $0.10 =
$_________
Hinge
$0.75 each
_______× $0.75 =
$_________
Dowel
$0.05 per inch
_______in × $0.05 =
$_________
Guitar string
$1.00 each
_______× $1.00 =
Final Material Total Cost(MTC)=
$_________
$
Percent of price excused (%EX)
o 2 distinct notes: Full price
o 3-5 distinct notes: 5% of final price excused
o 6-12 distinct notes: 10% of final price excused
o Over 12 distinct notes: 25% of final price excused
$______× _______%=$___________
Final Total cost:
$________- $ ________=___________
MTC
MTC
%EX
$exc.
$excused
Total
Teacher Notes:
I have set up the lab in such a way that students who do not know anything about music can
still create a good instrument (defining notes as frequencies). Although, if the teacher has any musical
knowledge to impart on the students, it may benefit them as well. Ideally this lab would spark interest
in engineering for students who are already interested in music. These students should be made aware
of sound engineering and related fields in the music (and general science) industry.
This lesson assumes that students are at least remotely familiar with an FFT scope and
understand what it does and how to take data from it. It may be to the students’ benefit to have a
chance to play around with the FFT scope and some Tuning Forks to see how it works (For example,
give students several tuning forks of different freq. and allow them to see that a large spike occurs in
the area of the frequency of the fork). This will familiarize them with the software and make the
experiment go more smoothly.
A big difference between calculated resulting frequencies and actual resulting frequencies will
come from the stretching of the string when it is tightened. If the resulting frequency does not match
the calculated, students will need to account for it in their final design and design problems sections.
They may need to be prodded to think of the assumptions they made. This small difference is typically
quite difficult for students to account for since, technically, the string length does not change, but when
the string is stretched, the linear mass density will change (though very slightly).
Students who finish quickly can be asked to make improvements to their design. For example,
if an instrument can only make one or two or even 12 notes, students can be asked to make the
instrument make more notes. It is possible for an instrument built with these materials, depending on
design, to make an infinite number of notes (or frequencies) For ideas, search for “fretless bass” or
“whamola” on Wikipedia.
Finally, it is important for students to realize that the cost of the instrument is not indicatory
of their grade on the assignment. Their grade will depend on the rubrics for an application experiment
(which they will have access to from the teacher website). So it is their work and accurate analysis of
assumptions and proper reasoning that will affect their grade for the assignment.
8. Time Table(2 Day lab or 1 day extended period)
Clock reading
during the lesson
0 - 5 min
5-10 min
10-35 min
“Title of the
activity”
Homework quiz,
receive feedback
Introduction,
statement of story
and materials
Initial research and
calculations
Students Doing
Teacher Doing
Writing
Checking up equipment for
the activity
Listening taking notes, Addressing class, showing
Getting into groups.
material
Using freq. gen. to find
desired frequencies.
Helping students with
questions or with software
issues.
Clock reading
during the lesson
35-45 min
“Title of the
activity”
Begin designing
45-75 min (0-30 min
if continuing on
another day)
Building, testing, and
redesign.
70 – 85 min (30-45
min next day)
Make changes and
evaluate
Students Doing
Teacher Doing
Looking at materials
and beginning to think
about design and how
they will achieve their
goal
Constructing
instrument and noting
changes that need to
be made to initial
design.
Finishing their design
and hopefully
achieving best results
after considering
assumptions
Approving of designs and
helping students realize
their ideas.
Helping students overcome
design hurdles. (see
Possible students
difficulties)
Helping students overcome
design hurdles. (see
Possible students
difficulties). Encouraging
step by step fixes. Assigning
homework.
9. Formative Assessments:
Content Goals:
 Observe that the angle of the projectile will affect maximum distance
 Correct calculation of uncertainties in average velocity and heights. Outcome reflects
consistency between result and prediction.
Process Goals:
 Detailed completion of the design handout
 Assessment through application experiment rubrics
 Ability to overcome problems will demonstrate that they are able to address small
problems one at a time rather than tear the whole thing apart and start over.
Epistemological Goals:
 Students’ ability to accurately and effectively analyze assumptions and explain what effect
this had on the final resulting frequency.
 Ability of students to effectively solve problems and hurdles in the design process.
 Students are able to effectively work in groups and no one individual is doing bulk of work.
 In homework, answers question relating engineering and physics effectively.
Metacognitive Goals:
 Ability to answer homework question on contribution to the team and design process.
 Ability to answer homework questions about how their instrument made different notes
(frequencies).
10.
Modification for different learners:
By nature of the course, different learners will automatically be accounted for. Students will be
working in groups, so the activity is already a cooperative learning activity. The activity could
utilize technology in the form of graphing or mathematical programs for learners who prefer the
organization of a computerized write-up. Bilingual or ELL students should have no difficulty as they
not only have peer instruction, but all concepts used in the lab have been previously addressed and
students are constructing new knowledge together. Since the teacher is not introducing new terms
or ideas, there is no risk of misunderstanding.
11.
Homework:
1) We saw today that, when we tried applying physics to our real life situation, the physics
was not always right(Which NEVER happens!) Based on this, what do you feel is the
difference between physics and engineering? What kind of problems do each group
have to deal with and what is their typical approach?
(Students should address how physicists will attempt to simplify the situation to ideal
terms to make the mathematics simpler and develop a model that MOST accurately
describes the situation, whereas engineers, who have to apply the physics in real life, have
to take these models as just models and deal with all the problems that the physicists
simplified away, see “spherical cow” joke…)
2) What difficulties did you have in the engineering and design process ? (List at least two)
How did you overcome these difficulties?
3) What was your contribution to the design process?
4) Stringed instruments make different frequencies by varying one of the variables in the
equations we’ve used. Which variable did your instrument change to change the
frequency?
5) The music company has decided to pick up your instrument and has decided it was so
good, you can use any resources you want to make it better. What would you do to
improve your design even more? (make it louder, aesthetic appearance, materials, etc).