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written by Andrzej Sokolowski
This high school lesson plan is intended to supplement the "Wave on a String" PhET simulation. Students apply the concepts introduced in the computer simulation to explore properties of sinusoidal functions. They will find an equation of a wave with pre-set components and analyze how amplitude, frequency, and tension influence changes in the wave motion. The activity is intended to take ~60 minutes to complete.

The wave simulation, which must be open and displayed to complete this activity, is available from PhET at: Wave on a String.

This lesson is part of PhET (Physics Education Technology Project), a large collection of free interactive simulations for science education.
Subjects Levels Resource Types
Education Practices
- Active Learning
= Modeling
Oscillations & Waves
- Oscillations
= Springs and Oscillators
- Wave Motion
= Transverse Pulses and Waves
- High School
- Instructional Material
= Activity
= Lesson/Lesson Plan
Appropriate Courses Categories Ratings
- Conceptual Physics
- Algebra-based Physics
- AP Physics
- Lesson Plan
- Activity
- Laboratory
- Assessment
- New teachers
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Keywords:
PhET, amplitude, frequency, lesson plans, string tension, waves
Record Cloner:
Metadata instance created April 17, 2008 by Caroline Hall
Record Updated:
August 18, 2016 by Lyle Barbato
Last Update
when Cataloged:
December 29, 2010

### AAAS Benchmark Alignments (2008 Version)

#### 4. The Physical Setting

4F. Motion
• 6-8: 4F/M4. Vibrations in materials set up wavelike disturbances that spread away from the source. Sound and earthquake waves are examples. These and other waves move at different speeds in different materials.
• 6-8: 4F/M7. Wave behavior can be described in terms of how fast the disturbance spreads, and in terms of the distance between successive peaks of the disturbance (the wavelength).
• 9-12: 4F/H6ab. Waves can superpose on one another, bend around corners, reflect off surfaces, be absorbed by materials they enter, and change direction when entering a new material. All these effects vary with wavelength.

#### 9. The Mathematical World

9B. Symbolic Relationships
• 9-12: 9B/H5. When a relationship is represented in symbols, numbers can be substituted for all but one of the symbols and the possible value of the remaining symbol computed. Sometimes the relationship may be satisfied by one value, sometimes by more than one, and sometimes not at all.

#### 11. Common Themes

11B. Models
• 6-8: 11B/M4. Simulations are often useful in modeling events and processes.
• 9-12: 11B/H1a. A mathematical model uses rules and relationships to describe and predict objects and events in the real world.

### Common Core State Standards for Mathematics Alignments

#### Standards for Mathematical Practice (K-12)

MP.4 Model with mathematics.

#### Expressions and Equations (6-8)

Represent and analyze quantitative relationships between dependent and independent variables. (6)
• 6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.

#### High School — Algebra (9-12)

Seeing Structure in Expressions (9-12)
• A-SSE.2 Use the structure of an expression to identify ways to rewrite it.
Creating Equations? (9-12)
• A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

#### High School — Functions (9-12)

Building Functions (9-12)
• F-BF.1.a Determine an explicit expression, a recursive process, or steps for calculation from a context.
• F-BF.1.c (+) Compose functions.
• F-BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
Trigonometric Functions (9-12)
• 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 the context.?

This resource is part of 2 Physics Front Topical Units.

Topic: Periodic and Simple Harmonic Motion
Unit Title: Simple Harmonic Motion

This high-quality lesson plan was created to be used with the PhET simulation "Wave on a String".  Students will apply the concepts introduced in the computer simulation to explore frequency, amplitude, and tension on an oscillating string. Editor's Note: this lesson gives students the chance to model the movement of energy on a string by applying properties of sinusoidal function. A great integration of trigonometry and physics.....and it's fun!

Topic: Wave Energy
Unit Title: Wave Properties: Frequency, Amplitude, Period, Phase

This is a computer lab created specifically for use with the PhET simulation "Wave on a String" (see Activities below).  Students apply trigonometry and analyze how frequency, amplitude, and tension influence the motion of the wave.  It  may be downloaded as a Word file.

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AIP Format
A. Sokolowski, (2010), WWW Document, (https://phet.colorado.edu/en/contributions/view/3340).
AJP/PRST-PER
A. Sokolowski, PhET Teacher Ideas & Activities: Applications of Sinusoidal Functions, (2010), <https://phet.colorado.edu/en/contributions/view/3340>.
APA Format
Sokolowski, A. (2010, December 29). PhET Teacher Ideas & Activities: Applications of Sinusoidal Functions. Retrieved December 11, 2016, from https://phet.colorado.edu/en/contributions/view/3340
Chicago Format
Sokolowski, Andrzej. PhET Teacher Ideas & Activities: Applications of Sinusoidal Functions. December 29, 2010. https://phet.colorado.edu/en/contributions/view/3340 (accessed 11 December 2016).
MLA Format
Sokolowski, Andrzej. PhET Teacher Ideas & Activities: Applications of Sinusoidal Functions. 2010. 29 Dec. 2010. 11 Dec. 2016 <https://phet.colorado.edu/en/contributions/view/3340>.
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@misc{ Author = "Andrzej Sokolowski", Title = {PhET Teacher Ideas & Activities: Applications of Sinusoidal Functions}, Volume = {2016}, Number = {11 December 2016}, Month = {December 29, 2010}, Year = {2010} }
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%A Andrzej Sokolowski
%T PhET Teacher Ideas & Activities: Applications of Sinusoidal Functions
%D December 29, 2010
%O application/ms-word

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%0 Electronic Source
%A Sokolowski, Andrzej
%D December 29, 2010
%T PhET Teacher Ideas & Activities: Applications of Sinusoidal Functions
%V 2016
%N 11 December 2016
%8 December 29, 2010
%9 application/ms-word

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### PhET Teacher Ideas & Activities: Applications of Sinusoidal Functions:

Is Supplemented By PhET Teacher Ideas & Activities: Wave Unit

This is a full unit of instruction for high school physics students on the topic of Waves.  It includes lesson plans, content support, chapter tests, homework problems, lecture presentations, and clicker questions.

relation by Lyle Barbato
Is Based On PhET Simulation: Wave on a String

The Wave on a String simulation is the basis for this activity.

relation by Lyle Barbato
Is Part Of PhET Teacher Ideas & Activities: Browse Activities

This is the full collection of teacher-created lesson plans and labs designed to be used with specific PhET simulations.  Each resource has been approved by the PhET project, and may be freely downloaded.

relation by Bruce Mason

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