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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.

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.^{?}

Sokolowski, A. (2010, December 29). PhET Teacher Ideas & Activities: Applications of Sinusoidal Functions. Retrieved July 29, 2016, from http://phet.colorado.edu/en/contributions/view/3340

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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.

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.