harmonic motion, waves, and sound wave...

Real Investigations in Science and Engineering

™

Wave ModelsHarmonic Motion, Waves, and Sound

WM_cover_final.indd 1 5/5/15 1:42 PM

Overview Chart for Investigations–Wave ModelsInvestigation Key Question Summary Learning Goals Vocabulary

A1 The PendulumPages 1–8100 minutes

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.

amplitudecycledampingharmonic motionoscillationoscillatorperiod

A2 Making a ClockPages 9–1450 minutes

How can you use a pendulum to measure time?

Students design a time-keeping pendulum. They choose a number of cycles to equal one minute for their 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.

• Use a graph to make predictions.• Build a pendulum clock that can

accurately measure one minute.

pendulum

A3 Making WavesPages 15–2050 minutes

What are some of the properties of waves?

Students use the Sound & Waves kit to create waves of different frequencies. By observing patterns in these waves, students identify harmonics and the fundamental. Finally, students discover that there is an inverse relationship between frequency and wavelength.

• Use the nodes and antinodes of a standing wave to determine the wave’s harmonic, frequency, and wavelength.

• Identify the relationship between frequency and wavelength.

direct relationshipfrequencyfundamentalharmonicinverse relationshipmediumstanding wavewavewavelength

A4 SoundPages 21–2650 minutes

What is sound and how do we hear it?

Students explore the relationship between the frequency and perception of sound. Using the Sound & Waves kit, students generate sounds of different frequencies and observe how those frequencies are detected by the human ear. These observations are then analyzed using a histogram to show students differences in human hearing.

• Identify the typical audible range for the human ear.

• Explain how the pitch of a note is related to the frequency of a sound wave.

histogramnotepitch

A5 MusicPages 27–3450 minutes

What is music and how is it made?

Students use the console to explore the connection between frequencies and the musical scale. They will play different frequencies of sound together and hear the difference between a major and minor chord. They also 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.

beatchordfrequencymusical scalenoteoctavepitch

xvi

WM_TG.indb 16 5/12/15 1:50 PM page 16


B1 Harmonic MotionPages 35–44200 minutes

How do we describe the back-and-forth motion of a pendulum?

Students are introduced to harmonic motion using a simple pendulum. They design and implement an experiment to determine which of three variables (length, mass, or amplitude) has the greatest influence on the period of the pendulum. They apply their analysis to design an accurate clock that measures 30 seconds.

• Measure the amplitude and period of a pendulum.

• Predict how the period of a pendulum changes using knowledge of physical parameters such as mass, amplitude, and string length.

• Design and build a clock to measure a 30-second time interval.

• Observe and describe damping and how it affects oscillators.

amplitudecycledampingharmonic motionoscillatorpendulumperiod

B2 The 5-Second PendulumPages 45–5050 minutes

What length of string would produce a 5-second pendulum?

Students use their data from the previous investigation to come up with an equation to calculate period from string length. They solve their equation for string length and then extrapolate the string length required for a 5-second pendulum. To complete their analysis, they compare their equation with Huygens’s derived equation for pendulum period.

• State a hypothesis that describes how string length and period are related.

• Graph the hypothesized relationship and use the graph to derive an equation for determining the period given the string length.

• Use the equation to predict the string length needed to create a 5-second pendulum.

best fit curveextrapolationfunctiongraphinverse relationshipperiod

B3 Harmonic Motion GraphsPages 51–5850 minutes

How do we make graphs of harmonic motion?

Students discuss and practice making several graphs of harmonic motion from provided data. The concept of superposition (although not specifically named) is introduced by having students create a graph that shows two harmonic motions added together. By graphing motions with a phase difference, connections are made between circular motion and harmonic motion.

• Construct graphs of harmonic motion.

• Interpret graphs of harmonic motion to determine phase, amplitude, and period.

• Use the concept of phase to describe the relationship between two examples of harmonic motion.

amplitudecycleequilibriumharmonic motionin phaseoscillationout of phaseperiodphase

B4 Standing WavesPages 59–6650 minutes

How do we describe waves?

Students apply a periodic force to a vibrating string to create and study standing waves. Students will discover that the standing wave patterns appear only at certain frequencies, and determine how those frequencies 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.

• Generate waves on a vibrating string.

• Determine the frequency and wavelength of each wave.

• Identify how frequency and wavelength are related.

amplitudeantinodefrequencyfundamentalharmonichertz (Hz)nodestanding wavewavelength

xviiGetting Started with Wave Models

WM_TG.indb 17 5/12/15 1:50 PM page 17


B5 Natural FrequencyPages 67–7250 minutes

How do natural frequency and resonance relate?

Students learn that the frequency at which objects tend to vibrate is called the natural frequency. They discover that when the force applied to a system matches its natural frequency, the resulting strong response is called resonance. They experiment with different string tensions to discover how to change the natural frequency of the system.

• Explain how natural frequency and resonance are related.

• Identify how to change the natural frequency of a system.

• Describe the relationship between the force applied to a system and the natural frequency of the system.

frequencynatural frequencyperiodic forceresonancerestoring forcestanding wavetension

B6 Properties of SoundPages 73–80100 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.

frequencyhertz (Hz)

B7 Musical SoundsPages 81–8850 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.

beatchordconsonancedissonanceflatmusical scalenoteoctavesharp

C1 Energy ConservationPages 89–94100 minutes

How can we use the law of energy conservation to analyze the motion of the pendulum?

Students consider the motion of a pendulum to determine where in the swing the potential and kinetic energies are greatest and least, and then use this information to predict the maximum velocity of the pendulum at different heights relative to an initial position.

• Describe the relationships between potential energy and kinetic energy in a system.

• Apply the law of conservation of energy to derive an equation for the maximum velocity of a pendulum.

• Experimentally verify the equation.

energykinetic energylaw of conservation of energy

potential energy

xviii

WM_TG.indb 18 5/12/15 1:50 PM page 18


C2 The Physical PendulumPages 95–10250–100 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.

• 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.

center of massmoment of inertiaperiodphysical pendulumsimple pendulum

C3 Properties of WavesPages 103–110100 minutes

How do we make standing waves and what are their properties?

Students explore the properties and characteristics of standing waves on a vibrating string. Students will discover that the standing wave patterns appear only at certain frequencies, and determine how those frequencies 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.

• Determine the frequency and wavelength of a vibrating string.

• Identify how frequency and wavelength are related.

• Explore open and closed boundary conditions for waves.

amplitudeantinodeboundaryfrequencyfundamentalharmonichertz (Hz)nodestanding wavewavelength

C4 Natural Frequency and ResonancePages 111–12050–100 minutes

Which variables affect natural frequency?

Students observe the natural frequency of a simple pendulum, then vibrate the pendulum at its natural frequency to observe resonance. Next, they investigate resonance in a vibrating string in the form of standing waves. They experiment with changing the string’s natural frequency to discover the relationship between its tension and natural frequency.

• Measure the natural frequency of a system.

• Determine ways to change the natural frequency of a system.

• Describe the relationship between the force applied to a system and the natural frequency of the system.

frequencynatural frequencyperiodic forceresonancerestoring forcestanding wavetension

xixGetting Started with Wave Models

WM_TG.indb 19 5/12/15 1:50 PM page 19

Next Generation Science Standards CorrelationCPO 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

* 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.

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

Developing and Using Models

A4, A5

NGSS Disciplinary Core

Ideas


PS4.A: Wave Properties A1, A2, A3, A4, A5, B1, B2, B3, B4, B5, B6, B7, C2, C3, C4

PS4.B: Electromagnetic Radiation

A4, A5

PS3.A: Definitions of Energy

C1

PS3.B: Conservation of Energy and Energy Transfer

C1

NGSS Crosscutting Concepts


Patterns A1, A2, A3

Structure and Function A4, A5

Cause and Effect B1, B2, B3, B4, B5, B6, B7, C2, C3, C4

Systems and System Models

C1

xx

WM_TG.indb 20 5/12/15 1:50 PM page 20

Common Core State Standards CorrelationCCSS-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 two quantities

A1, A2, A3

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 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.

C1

HSN.Q.A.2 Define appropriate quantities for the purpose of descriptive modeling. C1

HSN.Q.A.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. 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 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.

C1

xxiGetting Started with Wave Models

WM_TG.indb 21 5/12/15 1:50 PM page 21

harmonic motion, waves, and sound wave...

Documents