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#### Description:

This activity 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:

• Education > General

English

#### Access Privileges:

Public - Available to anyone

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Update Standards?

#### CCSS.Math.Practice.MP4: Common Core State Standards for Mathematics

Model with mathematics.

#### CCSS.Math.Content.6.EE.C: Common Core State Standards for Mathematics

Represent and analyze quantitative relationships between dependent and independent variables.

#### CCSS.Math.Content.6.EE.C.9: Common Core State Standards for Mathematics

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.

#### CCSS.Math.Content.HSA-SSE.A: Common Core State Standards for Mathematics

Interpret the structure of expressions

#### CCSS.Math.Content.HSA-SSE.A.2: Common Core State Standards for Mathematics

Use the structure of an expression to identify ways to rewrite it.

#### CCSS.Math.Content.HSA-CED.A: Common Core State Standards for Mathematics

Create equations that describe numbers or relationships

#### CCSS.Math.Content.HSA-CED.A.4: Common Core State Standards for Mathematics

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

#### CCSS.Math.Content.HSF-BF.A: Common Core State Standards for Mathematics

Build a function that models a relationship between two quantities

#### CCSS.Math.Content.HSF-BF.A.1: Common Core State Standards for Mathematics

Write a function that describes a relationship between two quantities ?

#### CCSS.Math.Content.HSF-BF.A.1a: Common Core State Standards for Mathematics

Determine an explicit expression, a recursive process, or steps for calculation from a context.

#### CCSS.Math.Content.HSF-BF.A.1c: Common Core State Standards for Mathematics

(+) Compose functions.

#### CCSS.Math.Content.HSF-BF.B: Common Core State Standards for Mathematics

Build new functions from existing functions

#### CCSS.Math.Content.HSF-BF.B.3: Common Core State Standards for Mathematics

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.

#### CCSS.Math.Content.HSF-TF.B: Common Core State Standards for Mathematics

Model periodic phenomena with trigonometric functions

#### CCSS.Math.Content.HSF-TF.B.5: Common Core State Standards for Mathematics

Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.?

#### CCSS.Math.Content.HSF-TF.B.7: Common Core State Standards for Mathematics

(+) 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.?
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