Download Harmonic Motion, Waves, and Sound Wave Models

Harmonic Motion, Waves, and Sound
Wave Models
™
Real Investigations in
Science and Engineering
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Overview Chart for Investigations–Wave Models
Investigation
Key Question
Summary
Learning Goals
A1
The Pendulum
Pages 1–8
100 minutes
A2
Vocabulary
How can you
change the period
of a pendulum?
Students learn the vocabulary used
to describe harmonic motion. They
build pendulums and experiment
with three independent variables to
explore which has the greatest effect
on the period of a pendulum: mass,
amplitude, or string length.
• Learn terms used to describe
harmonic motion.
• Practice testing a system with
three independent variables.
• Graph pendulum data.
• Draw valid conclusions based on
data.
Making a Clock
Pages 9–14
50 minutes
How can you use
a pendulum to
measure time?
Students design a time-keeping
• Use a graph to make predictions. pendulum
pendulum. They choose a number of • Build a pendulum clock that can
cycles to equal one minute for their
accurately measure one minute.
pendulum, then determine the length
of the pendulum’s period. Based on
the period, they select the length of
pendulum string needed. Students
build their pendulum clocks and test
their accuracy with a stopwatch.
A3
Making Waves
Pages 15–20
50 minutes
What are some of
the properties of
waves?
Students use the Sound & Waves kit to • Use the nodes and antinodes of a
create waves of different frequencies.
standing wave to determine the
By observing patterns in these waves,
wave’s harmonic, frequency, and
students identify harmonics and
wavelength.
the fundamental. Finally, students
• Identify the relationship between
discover that there is an inverse
frequency and wavelength.
relationship between frequency and
wavelength.
A4
Sound
Pages 21–26
50 minutes
What is sound and
how do we hear it?
Students explore the relationship
• Identify the typical audible range histogram
between the frequency and
for the human ear.
note
perception of sound. Using the Sound • Explain how the pitch of a note
pitch
& Waves kit, students generate sounds is related to the frequency of a
of different frequencies and observe
sound wave.
how those frequencies are detected
by the human ear. These observations
are then analyzed using a histogram
to show students differences in
human hearing.
A5
Music
Pages 27–34
50 minutes
What is music and
how is it made?
Students use the console to explore
• Make musical notes by changing
the connection between frequencies
the frequencies of sound.
and the musical scale. They will play
• Describe how to make a major
different frequencies of sound together
chord and a minor chord.
and hear the difference between a
• Calculate the frequency of a note
major and minor chord. They also
in a higher or lower octave.
learn how to calculate the frequencies
of notes in different octaves of the
musical scale.
amplitude
cycle
damping
harmonic motion
oscillation
oscillator
period
direct relationship
frequency
fundamental
harmonic
inverse relationship
medium
standing wave
wave
wavelength
beat
chord
frequency
musical scale
note
octave
pitch
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Overview Chart for Investigations–Wave Models
Investigation
Key Question
Summary
Learning Goals
Vocabulary
B1
Harmonic Motion How do we describe
the back-andPages 35–44
forth motion of a
200 minutes
pendulum?
Students are introduced to harmonic • Measure the amplitude and
motion using a simple pendulum.
period of a pendulum.
They design and implement an
• Predict how the period of
experiment to determine which of
a pendulum changes using
three variables (length, mass, or
knowledge of physical
amplitude) has the greatest influence
parameters such as mass,
on the period of the pendulum.
amplitude, and string length.
They apply their analysis to design
• Design and build a clock to
an accurate clock that measures 30
measure a 30-second time
seconds.
interval.
• Observe and describe damping
and how it affects oscillators.
amplitude
cycle
damping
harmonic motion
oscillator
pendulum
period
B2
The 5-Second
Pendulum
Pages 45–50
50 minutes
Students use their data from the
• State a hypothesis that describes
previous investigation to come up
how string length and period are
with an equation to calculate period
related.
from string length. They solve their
• Graph the hypothesized
equation for string length and then
relationship and use the graph
extrapolate the string length required
to derive an equation for
for a 5-second pendulum. To complete
determining the period given the
their analysis, they compare their
string length.
equation with Huygens’s derived
• Use the equation to predict the
equation for pendulum period.
string length needed to create a
5-second pendulum.
best fit curve
extrapolation
function
graph
inverse relationship
period
B3
Harmonic Motion How do we make
graphs of harmonic
Graphs
motion?
Pages 51–58
50 minutes
Students discuss and practice making • Construct graphs of harmonic
several graphs of harmonic motion
motion.
from provided data. The concept
• Interpret graphs of harmonic
of superposition (although not
motion to determine phase,
specifically named) is introduced by
amplitude, and period.
having students create a graph that
• Use the concept of phase
shows two harmonic motions added
to describe the relationship
together. By graphing motions with
between two examples of
a phase difference, connections are
harmonic motion.
made between circular motion and
harmonic motion.
amplitude
cycle
equilibrium
harmonic motion
in phase
oscillation
out of phase
period
phase
B4
Standing Waves
Pages 59–66
50 minutes
What length of
string would
produce a 5-second
pendulum?
How do we describe Students apply a periodic force to a
• Generate waves on a vibrating
waves?
vibrating string to create and study
string.
standing waves. Students will discover • Determine the frequency and
that the standing wave patterns
wavelength of each wave.
appear only at certain frequencies,
• Identify how frequency and
and determine how those frequencies
wavelength are related.
are related. Students discover the
relationship between wavelength
and frequency and that the speed of
a wave is the product of its frequency
and its wavelength.
amplitude
antinode
frequency
fundamental
harmonic
hertz (Hz)
node
standing wave
wavelength
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Overview Chart for Investigations–Wave Models
Investigation
Key Question
Summary
Learning Goals
Vocabulary
B5
Natural
Frequency
Pages 67–72
50 minutes
How do natural
frequency and
resonance relate?
Students learn that the frequency at
• Explain how natural frequency
which objects tend to vibrate is called
and resonance are related.
the natural frequency. They discover
• Identify how to change the
that when the force applied to a
natural frequency of a system.
system matches its natural frequency, • Describe the relationship
the resulting strong response is called
between the force applied to a
resonance. They experiment with
system and the natural frequency
different string tensions to discover
of the system.
how to change the natural frequency of
the system.
frequency
natural frequency
periodic force
resonance
restoring force
standing wave
tension
B6
Properties of
Sound
Pages 73–80
100 minutes
What is sound and
how do we hear it?
Students explore the properties of
sound. Humans hear frequencies
between 20 and 20,000 hertz, but the
actual range that is heard varies with
each individual. Students discover this
by measuring their own sensitivity to
sound as well as the sensitivity of their
classmates. In the process, students
learn how to design an unbiased
experiment.
• Determine the range in human
perception of sound.
• Distinguish between absolute
and relative difference in sound
frequencies.
• Identify the advantages of good
experimental design.
frequency
hertz (Hz)
B7
Musical Sounds
Pages 81–88
50 minutes
Why do we like
some sounds and
dislike others?
Students use the console to discover
why certain frequencies sound good
together while others do not. They
also explore the connection between
frequencies and the musical scale.
Groups of students play different
frequencies of sound together and
hear the difference between a major
and minor chord. Finally, they learn
how to calculate the frequencies
of notes in different octaves of the
musical scale.
• Make musical notes by changing
the frequencies of sound.
• Describe how to make a major
chord and a minor chord.
• Calculate the frequency of a note
in a higher or lower octave.
• Calculate frequencies of all of the
notes in a scale using ratios.
beat
chord
consonance
dissonance
flat
musical scale
note
octave
sharp
C1
Energy
Conservation
Pages 89–94
100 minutes
How can we use
the law of energy
conservation to
analyze the motion
of the pendulum?
Students consider the motion of a
• Describe the relationships
pendulum to determine where in
between potential energy and
the swing the potential and kinetic
kinetic energy in a system.
energies are greatest and least,
• Apply the law of conservation
and then use this information to
of energy to derive an equation
predict the maximum velocity of the
for the maximum velocity of a
pendulum at different heights relative
pendulum.
to an initial position.
• Experimentally verify the
equation.
energy
kinetic energy
law of conservation
of energy
potential energy
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Overview Chart for Investigations–Wave Models
Investigation
Key Question
Summary
Learning Goals
C2
The Physical
Pendulum
Pages 95–102
50–100 minutes
Which model
best predicts the
period of a physical
pendulum?
Students expand their study of the
pendulum. They study a physical
pendulum and measure its period.
They calculate the period using
the expressions for the period of a
simple pendulum and for a thin rod
pendulum. They compare predicted
and measured values to determine
which mathematical model best
represents the physical pendulum.
C3
Properties of
Waves
Pages 103–110
100 minutes
How do we make
standing waves
and what are their
properties?
Students explore the properties and • Determine the frequency and
characteristics of standing waves on a
wavelength of a vibrating string.
vibrating string. Students will discover • Identify how frequency and
that the standing wave patterns
wavelength are related.
appear only at certain frequencies,
• Explore open and closed
and determine how those frequencies
boundary conditions for waves.
are related. Students discover the
relationship between wavelength
and frequency and that the speed of
a wave is the product of its frequency
and its wavelength.
amplitude
antinode
boundary
frequency
fundamental
harmonic
hertz (Hz)
node
standing wave
wavelength
C4
Natural
Frequency and
Resonance
Pages 111–120
50–100 minutes
Which variables
affect natural
frequency?
Students observe the natural
• Measure the natural frequency of
frequency of a simple pendulum, then
a system.
vibrate the pendulum at its natural
• Determine ways to change the
frequency to observe resonance.
natural frequency of a system.
Next, they investigate resonance
• Describe the relationship
in a vibrating string in the form of
between the force applied to a
standing waves. They experiment
system and the natural frequency
with changing the string’s natural
of the system.
frequency to discover the relationship
between its tension and natural
frequency.
frequency
natural frequency
periodic force
resonance
restoring force
standing wave
tension
• Evaluate the usefulness of the
expression for the period of a
simple pendulum in predicting
the period of a physical
pendulum.
• Describe the effect of adding
mass to a physical pendulum at
various points along its length.
Vocabulary
center of mass
moment of inertia
period
physical pendulum
simple pendulum
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Getting Started with Wave Models
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Next Generation Science Standards Correlation
CPO Science Link investigations are designed for successful implementation of the Next Generation Science Standards. The
following chart shows the NGSS Performance Expectations and dimensions that align to the investigations in this title.
NGSS Performance Expectations
Wave Models Investigations
MS-PS4-1. Use mathematical representations to describe a simple model for waves that includes how the
amplitude of a wave is related to the energy in a wave.
A1, A2, A3
MS-PS4-2. Develop and use a model to describe that waves are reflected, absorbed, or transmitted
through various materials.
A4, A5
HS-PS4-1. Use mathematical representations to support a claim regarding relationships among the
frequency, wavelength, and speed of waves traveling in various media.
B1, B2, B3, B4, B5, B6, B7, C2, C3, C4
HS-PS3-1. Create a computational model to calculate the change in the energy of one component in a
system when the change in energy of the other component(s) and energy flows in and out
of the system are known.
C1
NGSS
Science and
Engineering
Practices
Wave Models
Investigations
Using Mathematics
and Computational
Thinking
A1, A2, A3, B1, B2,
B3, B4, B5, B6, B7,
C1, C2, C3, C4
PS4.A: Wave Properties A1, A2, A3, A4, A5,
B1, B2, B3, B4, B5,
B6, B7, C2, C3, C4
Patterns
Developing and Using
Models
A4, A5
PS4.B: Electromagnetic A4, A5
Radiation
Structure and Function A4, A5
PS3.A: Definitions of
Energy
C1
Cause and Effect
B1, B2, B3, B4, B5,
B6, B7, C2, C3, C4
PS3.B: Conservation
of Energy and Energy
Transfer
C1
Systems and System
Models
C1
NGSS
Disciplinary Core
Ideas
Wave Models
Investigations
NGSS Crosscutting
Concepts
Wave Models
Investigations
A1, A2, A3
*
Next Generation Science Standards is a registered trademark of Achieve. Neither Achieve nor the lead states and partners that
developed the Next Generation Science Standards was involved in the production of, and does not endorse, this product.
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Common Core State Standards Correlation
CCSS-Mathematics
Wave Models Investigations
MP.2
Reason abstractly and quantitatively.
A1, A2, A3, B1, B2, B3, B4, B5, B6,
B7, C2, C3, C4
MP.4
Model with mathematics.
A1, A2, A3, B1, B2, B3, B4, B5, B6,
B7, C2, C3, C4
RP.A.1
Understand the concept of a ratio and use ratio language to describe a ratio relationship between A1, A2, A3
two quantities
RP.A.2
Recognize and represent proportional relationships between quantities.
A1, A2, A3
6.RP.A.3
Use ratio and rate reasoning to solve real-world and mathematical problems.
A1, A2, A3
HSN.Q.A.1
C1
HSN.Q.A.2
Use units as a way to understand problems and to guide the solution of multi-step problems;
choose and interpret units consistently in formulas; choose and interpret the scale and the origin
in graphs and data displays.
Define appropriate quantities for the purpose of descriptive modeling.
HSN.Q.A.3
Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. C1
C1
HSA.SSE.A.1 Interpret expressions that represent a quantity in terms of its context.
B1, B2, B3, B4, B5, B6, B7, C2, C3, C4
HSA.SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the
quantity represented by the expression.
B1, B2, B3, B4, B5, B6, B7, C2, C3, C4
HSA.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving
equations.
B1, B2, B3, B4, B5, B6, B7, C2, C3, C4
CCSS-English Language Arts & Literacy
Wave Models Investigations
SL.8.5
Integrate multimedia and visual displays into presentations to clarify information, strengthen
claims and evidence, and add interest.
A1, A2, A3, A4, A5
RST.11-12.7
Integrate and evaluate multiple sources of information presented in diverse formats and media
(e.g., quantitative data, video, multimedia) in order to address a question or solve a problem.
B1, B2, B3, B4, B5, B6, B7, C2, C3, C4
SL.11-12.5
C1
Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive
elements) in presentations to enhance understanding of findings, reasoning, and evidence and to
add interest.
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Getting Started with Wave Models
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