November 11, 2016

This model simulates the wave generating machine created by John Shive at Bell Laboratories and made famous by the Similarities in Wave Behavior film. The machine consists of horizontal cross-bars welded to a central wire spine that is perpendicular to the bars. The spine was constructed so that it can freely twist, allowing the cross-bars to produce wave-like patterns. The simulation allows various pulse shapes to be sent down the machine by selecting a function for the twist of the first rod or by dragging the first rod. The far end of the wave machine can be free or fixed, which changes the nature of the reflected wave. Change the lengths of the bars to simulate the effect of a wave propagating in a non-uniform medium. The original film that introduced Dr. Shive's wave generating machine can be viewed at no cost: Film: Similarities of Wave Behavior (AT&T Archives and History Collection). The Wave Machine model was created using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive.

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Model with mathematics.

Create equations that describe numbers or relationships

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.

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

Interpret functions that arise in applications in terms of the context

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.?

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.?

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.?