November 11, 2016

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.

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Model with mathematics.

Represent and analyze quantitative relationships between dependent and independent variables.

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.

Interpret the structure of expressions

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

Create equations that describe numbers or relationships

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

Build a function that models a relationship between two quantities

Write a function that describes a relationship between two quantities ?

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

(+) Compose functions.

Build new functions from existing functions

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.

Model periodic phenomena with trigonometric functions

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

(+) 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.?