The Wave Machine model simulates the wave machine produced by John Shive at Bell Laboratories and made famous by the PSSC Simple Waves film. The machine consists of horizontal bars welded to a torsion rod that is perpendicular to the bars. The simulation allows the user to change the lengths of the bars, thereby simulating the effect of a wave propagating in a non-uniform medium.

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. For example, applying a Gaussian twist produces a Gaussian traveling pulse but the width of this pulse depends on the wave speed. The far end of the wave machine can be free or clamped and this changes the nature of the reflected wave.

The Wave Machine model is a supplemental simulation for the article "Standing Waves in a Nonuniform Medium" by Paul Gluck in The Physics Teacher 49(2), 76-77 (2011) and has been approved by the authors and The Physics Teacher editor. 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. Double clicking the ejs_mech_osc_chains_WaveMachine.jar file will run the program if Java is installed.

Please note that this resource requires
at least version 1.5 of Java.

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.

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.

9-12: 4F/H6c. The energy of waves (like any form of energy) can be changed into other forms of energy.

9. The Mathematical World

9C. Shapes

9-12: 9C/H3c. A graph represents all the values that satisfy an equation, and if two equations have to be satisfied at the same time, the values that satisfy them both will be found where the graphs intersect.

11. Common Themes

11B. Models

6-8: 11B/M4. Simulations are often useful in modeling events and processes.

6-8: 11B/M5. The usefulness of a model depends on how closely its behavior matches key aspects of what is being modeled. The only way to determine the usefulness of a model is to compare its behavior to the behavior of the real-world object, event, or process being modeled.

Common Core State Standards for Mathematics Alignments

Standards for Mathematical Practice (K-12)

MP.4 Model with mathematics.

High School — Algebra (9-12)

Creating Equations^{?} (9-12)

A-CED.3 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.

A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

High School — Functions (9-12)

Interpreting Functions (9-12)

F-IF.4 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.^{?}

F-IF.6 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.

Building Functions (9-12)

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.^{?}

W. Christian and L. Wee, Computer Program WAVE MACHINE JS MODEL, Version 1.0 (2023), WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16530&DocID=5725).

W. Christian and L. Wee, Computer Program WAVE MACHINE JS MODEL, Version 1.0 (2023), <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16530&DocID=5725>.

Christian, W., & Wee, L. (2023). Wave Machine JS Model (Version 1.0) [Computer software]. Retrieved July 19, 2024, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16530&DocID=5725

Christian, Wolfgang, and Loo Kang Wee. "Wave Machine JS Model." Version 1.0. https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16530&DocID=5725 (accessed 19 July 2024).

%A Wolfgang Christian %A Loo Kang Wee %T Wave Machine JS Model %D August 19, 2023 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16530&DocID=5725 %O 1.0 %O text/html

%0 Computer Program %A Christian, Wolfgang %A Wee, Loo Kang %D August 19, 2023 %T Wave Machine JS Model %7 1.0 %8 August 19, 2023 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16530&DocID=5725

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