From The Physics Classroom’s Teacher Toolkit http://www.physicsclassroom.com/Teacher-Toolkits

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Teacher Toolkit

Topic:

Describing Waves

Objectives:

1. Describe the nature of a wave as a disturbance that moves through a medium,

transporting energy without transporting matter.

2. Distinguish local particle vibrations from overall wave motion and relate these

distinctions to types of waves such as longitudinal, transverse and surface waves.

3. Demonstrate understanding of wave properties such as wavelength, amplitude,

frequency, period, and speed and mathematically relate these properties to one another.

4. Apply the relationship among wave speed, frequency, and wavelength to solve

problems.

5. Build understanding of the relationship between energy and amplitude.

Readings:

The Physics Classroom Tutorial, Waves Chapter, Lesson 1

http://www.physicsclassroom.com/class/waves/Lesson-1/Waves-and-Wavelike-Motion

The Physics Classroom Tutorial, Waves Chapter, Lesson 2

http://www.physicsclassroom.com/class/waves/Lesson-2/The-Anatomy-of-a-Wave

Interactive Simulations:

1. PhET Simulation: Wave on a String

http://phet.colorado.edu/en/simulation/wave-on-a-string

Wiggle the string to create a wave. Set frequency, amplitude,

and tension and watch the results…..or manually generate the

disturbance. You can choose fixed, loose, or no end.

2. Wave Representations Model

http://www.opensourcephysics.org/items/detail.cfm?ID=7618

A flexible model that displays motion of a wave on a string

alongside Displacement/Time graph for two points on the

string. Using only these representations, you can determine

amplitude, period, wavelength, and wave speed. Run as a

simulation or customize for your class. Worksheet included.

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3. PhET Simulation: Fourier-Making Waves

http://phet.colorado.edu/en/simulation/fourier

More advanced simulation lets learners create different kinds

of waves by adding sines or cosines. Developed to promote

understanding of Fourier functions and help students become

comfortable with mathematical expressions for waves.

(Great resource for gifted/talented.)

Video and Animation:

1. Longitudinal/Transverse Wave Motion

http://www.acs.psu.edu/drussell/Demos/waves/wavemotion.html

Simple, yet very effective way to visualize the motion of

four types of waves: longitudinal, transverse, water, and

Rayleigh surface waves. Clearly shows how the wave

motion is not the same as the motion of particles in the

medium.

2. LivePhoto Physics: Wave Pulse Propagation on a Slinky Spring

http://livephoto.rit.edu/LPVideos/Slinky/

Easily downloadable short video clips of wave pulses on a

slinky spring, all shot with high-speed videography allowing

frame-by-frame stepping. The videos are very suitable for

video analysis. Collect position and time date with free

Tracker Video Analysis tool:

www.cabrillo.edu/~dbrown/tracker/

3. Internet Archive: Tacoma Narrows Bridge Collapse

https://archive.org/details/SF121

Dramatic 2.5-minute original footage of the 1940 collapse of the

Tacoma Narrows Bridge in Washington. Winds gusting at 42

mph drove the span into large-amplitude oscillatory motion.

Labs and Investigations:

1. The Physics Classroom, The Laboratory, A Wiggle in Time

http://www.physicsclassroom.com/lab - waves

Students observe and describe the motion of a mass on the end of a spring. Using a

motion detector, they describe the motion with words, with graphs, and in mathematical

terms.

2. The Physics Classroom, The Laboratory, A Wiggle in Time and Space

http://www.physicsclassroom.com/lab - waves

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Students explore the connection between a mass vibrating on a spring and a collection of

particles vibrating back and forth about a fixed position along the medium as a wave

passes through the medium.

3. The Physics Classroom, The Laboratory, Wave Motion

http://www.physicsclassroom.com/lab - waves

Students observe simulations and observe the difference between longitudinal,

transverse and surface waves.

4. The Physics Classroom, The Laboratory, Speed of a Wave

http://www.physicsclassroom.com/lab - waves

Students investigate the variables that do and do not affect the speed of a wave.

Demonstration Ideas:

1. Waves With Trolleys

Highly visual demo uses dynamics trolleys, springs, and spring holders to model

transverse and longitudinal waves. Easy set-up, yet allows exploration of complex

concepts such as how a dispersive system differs from a continuous wave medium like a

rope or slinky. Developed by Practical Physics.

Source: http://www.nuffieldfoundation.org/practical-physics/waves-trolleys

2. Wave Motion Machine

An oldie but goodie….this 28-minute historic film features physicist John Shive

demonstrating his torsional “wave machine” at Bell labs. Watch wave reflection from

fixed and free ends, wave superposition, standing waves, and wave impedance. If time is

limited, start the video at 6 minutes and watch to 11 minutes. Students can see the real-

life wave motion and compare it to the simulations.

Source: http://techchannel.att.com/play-video.cfm/2011/3/7/AT&T-Archives-Similarities-of-Wave-Behavior

Minds On Physics Internet Modules:

The Minds On Physics Internet Modules are a collection of interactive questioning modules

that target a student’s conceptual understanding. Each question is accompanied by detailed

help that addresses the various components of the question.

1. Waves module, Assignment WM1 – Nature and Categories of Waves

2. Waves module, Assignment WM2 – Wave Characteristics

3. Waves module, Assignment WM3 – Speed of a Wave

Source: http://www.physicsclassroom.com/mop

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Conceptual Building Exercises:

1. The Physics Classroom, Curriculum Corner, Wave Basics, Waves

2. The Physics Classroom, Curriculum Corner, Wave Basics, Describing Waves

3. The Physics Classroom, Curriculum Corner, Wave Basics, Wave Speed

Source: http://www.physicsclassroom.com/curriculum/waves

Problem-Solving Exercises:

1. The Physics Classroom, The Calculator Pad, Wave Basics, Problems #1-17

Source: http://www.physicsclassroom.com/calcpad/waves

Science Reasoning Activities:

1. The Physics Classroom, Science Reasoning Center, Waves: Mass on a Spring

Source: http://www.physicsclassroom.com/reasoning/waves

Real Life Connections:

1. Modeling the 2004 Indian Ocean Tsunami for Introductory Physics Students

http://www.jcu.edu/educatio/greg/Research/Tsunami/Tsunami_article.pdf

A “how-to” article on building a simple tank to model the motion of a tsunami wave,

plus explicit instructions on how to create an impulsive disturbance in the tank to

simulate an earthquake that will, in turn, generate a tsunami-like wave in the 6-foot

trough.

Common Misconceptions

1. What Moves?

It is common for students to believe that waves involve the transport of matter from the

source to a distant location. Emphasize that waves do not transport matter. What one

sees as a wave moves through a Slinky

TM

or water is the movement of a pattern of crests

and troughs (or compressions and rarefactions); this results in the movement of energy

without any movement of matter. Particles within the medium (i.e., matter) simple

vibrate back-and-forth about a fixed position.

2. Confusion of Frequency and Speed

Students often confuse the concepts of wave frequency and wave speed. Wave speed

refers to how fast a wave moves and is related to the distance traveled by a point on a

wave per unit of time. Speed is much different than frequency. Frequency describes how

often particles of the medium undergo vibrations about their fixed position. A medium

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in which particles vibrate frequently about a fixed position is not necessarily a fast wave.

Be cautious of your own use of the terms frequency and speed and monitor the language

of students and gently correct those who describe frequent vibrations as fast.

Elsewhere on the Web:

Student Difficulties with Wave Concepts

http://www.physics.umd.edu/perg/papers/wittmann/seminartalk/index.htm

A must-read presentation by Michael Wittmann, physics professor and team member of

the University of Maryland PER (Physics Education Research Group). The resource is

freely accessible as a set of 44 slides, exported from Power Point to html to support ease

of user download. See the results of research on how students formulate mental models

of waves concepts and learn to recognize common misconceptions.

Standards:

A. Next Generation Science Standards (NGSS) – Grades 9-12

Disciplinary Core Ideas

• High School-PS4.A.i The wavelength and frequency of a wave are related to one

another by the speed of travel of the wave, which depends on the type of wave and the

medium through which it is passing.

• High School-PS4.A.iii Waves can add or cancel one another as they cross, depending

on their relative phase (i.e., relative position of peaks and troughs of the waves), but

they emerge unaffected by each other.

• Middle School-PS4.A.i A simple wave has a repeating pattern with a specific

wavelength, frequency, and amplitude.

Performance Expectations

• Middle School 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.

• Middle School PS4-2 Develop and use a model to describe that waves are reflected,

absorbed, or transmitted through various materials.

• High School PS4-1 Use mathematical representations to support a claim regarding

relationships among the frequency, wavelength, and speed of waves traveling in various

media.

Science and Engineering Practices (SEPs)

Practice #1: Developing and Using Models

• Develop and/or use multiple types of models to provide mechanistic accounts and/or

predict phenomena, and move flexibly between model types based on merits and

limitations.

• Develop and/or use a model (including mathematical and computational) to generate

data to support explanations, predict phenomena, analyze systems, and/or solve

problems.

Practice #3: Planning and Carrying Out Investigations

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• Plan and conduct an investigation individually and collaboratively to produce data to

serve as the basis for evidence, and in the design: decide on types, how much, and

accuracy of data needed to produce reliable measurements and consider limitations on the

precision of the data (e.g., number of trials, cost, risk, time), and refine the design

accordingly.

Practice #4: Analyzing Data

• Compare and contrast various types of data sets (e.g., self-generated, archival) to

examine consistency of measurements and observations.

Practice #5: Using Mathematics and Computational Thinking

• Create and/or revise a computational model or simulation of a phenomenon, designed

device, process, or system.

• Apply techniques of algebra and functions to represent and solve scientific and

engineering problems.

Practice #6: Constructing Explanations

• Construct and revise an explanation based on valid and reliable evidence obtained

from a variety of sources (including students’ own investigations, models, theories,

simulations, peer review) and the assumption that theories and laws that describe the

natural world operate today as they did in the past and will continue to do so in the

future.

Practice #8: Obtaining, Evaluating, and Communicating Information

• Critically read scientific literature adapted for classroom use to determine the central

ideas or conclusions and/or to obtain scientific and/or technical information to

summarize complex evidence, concepts, processes, or information presented in a text

by paraphrasing them in simpler but still accurate terms.

• Compare, integrate and evaluate sources of information presented in different media or

formats (e.g., visually, quantitatively) as well as in words in order to address a

scientific question or solve a problem.

B. Common Core Standards (CC) – Grades 9-12 Mathematics

Standards for Mathematical Practice

• Reason abstractly and quantitatively

• Model with mathematics

High School – Number and Quantity: Quantities

• N-Q.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.

High School – Algebra: Interpret the Structure of Expressions

• A-SSE.2 Use the structure of an expression to identify ways to rewrite it.

High School – Algebra: Represent and Solve Equations and Inequalities Graphically

• A-REI.10 Understand that the graph of an equation in two variables is the set of all

its solutions plotted in the coordinate plane, often forming a curve.

High School – Functions: Interpret Functions that Arise in Applications in Terms of the

Context

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• F-IF.5 Relate the domain of a function to its graph and, where applicable, to the

quantitative relationship it describes.

• F-IF.6 Calculate and interpret the average rate of change of a function (presented

symbolically or as a table) over a specified interval. Estimate the rate of change from a

graph.

High School – Functions: Compare Properties of Two Functions

• F-IF.9 Compare properties of two functions each represented in a different way

(algebraically, graphically, numerically in tables, or by verbal descriptions).

High School – Trigonometric Functions: Model Periodic Phenomena

• F-TF.5 Choose trigonometric functions to model periodic phenomena with

specified amplitude, frequency, and midline.

• F-TF.7 Use inverse functions to solve trigonometric equations that arise in

modeling contexts, evaluate the solutions using technology, and interpret them in

terms of a context.

C. Common Core Standards (CC) – Grades 9-12 English/Language Arts

High School – Reading Standards for Literacy in Science and Technical Subjects

• RST.11-12.2 Determine the central ideas of conclusions of a text; summarize

complex concepts, processes, or information presented in a text by paraphrasing them

in simpler but still accurate terms.

• RST.11-12.4 Determine the meaning of symbols, key terms, and other domain-

specific words and phrases as they are used in a specific scientific or technical context

relevant to grades 11-12 texts and topics.

• 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 problem.

• RST.11-12.9 Synthesize information from a range of sources (e.g., texts,

experiments, simulations) into a coherent understanding of a process, phenomenon, or

concept, resolving conflicting information when possible.

• RST.9-12.10 By the end of Grade 10, read and comprehend science/technical texts

in the grades 11-CCR text complexity band independently and proficiently.

D. College Ready Physics Standards (Heller and Stewart)

Objective 4.3 Mechanical Wave Interactions and Energy

Middle School: A mechanical wave interaction occurs when a vibrating object (energy

source) produces a wave disturbance that travels through a material (medium). This wave

disturbance transfers energy to an object at a distance (energy receiver) by displacing the

material, but not transferring it. Although the material is temporarily displaced, it returns

to its original (undisturbed) position. (M.4.3.1)

• A mechanical wave requires a material (solid, liquid, or gas) in which to travel and is

characterized by three variables: frequency, wavelength, and amplitude.

• There are two primary types of waves: transverse waves (e.g. ropes) and compression

(longitudinal) waves (e.g., slinky, sound waves). Some waves, such as seismic waves,

have both components.

• For a given material (medium), the amount of energy transfer during mechanical wave

interaction during a defined time interval depends on the frequency and amplitude of

the vibrating energy source.

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• A wave disturbance travels approximately at a constant speed through a uniform

material (medium). The speed of the wave depends on the nature of the material (e.g.,

the wave travels faster through a solid than through a gas). As the frequency (f) of a

wave through a material increases, the wavelength of the wave decreases.