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Wave Machine Model
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 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.
Please note that this resource requires
at least version 1.5 of
Wave Machine Source Code
The source code zip archive contains an XML representation of the Wave Machine model. Unzip this archive in your EJS workspace to compile and run this model using EJS. download 38kb .zip
Last Modified: August 28, 2012
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
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
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.?
This resource is part of a Physics Front Topical Unit.
Topic: Wave Energy Unit Title: Standing Waves and Resonance
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 simulation produces sinusoidal waves by twisting the first rod with a given frequency and amplitude. Students can set the end to be free or fixed, select a function for twisting the first rod, add a damping force, or change the length of the bars to visualize how a wave propagates in a non-uniform medium. Graphs are displayed that plot mechanical energy as a function of frequency. Advanced students can compute the speed of the traveling waves at various frequencies and plot dispersion curves.
%0 Computer Program %A Christian, Wolfgang %D November 10, 2010 %T Wave Machine Model %7 1.0 %8 November 10, 2010 %U http://www.compadre.org/Repository/document/ServeFile.cfm?ID=10481&DocID=1936
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