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A Gaussian pulse propagating on a Shive wave machine with 64 rods.

Wave Machine

Twisting a bar about the torsion rod causes the bar to oscillate because the rod produces a restoring torque. Because a bar twist acts on neighboring bars, the motions are coupled and a traveling wave results. The speed of the wave depends on the torsional coupling between bars k and the moments of inertia of the bars. A damping force can also be added using the model's damping parameter b.

The simulation allows various pulse shapes to be sent down the machine by twisting the first rod with the desired functional form 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.

Theoretical note: The pulse shape will distort as the wave propagates on the wave machine because of dispersion effects. This distortion is most apparent as the wavelength (or pulse width) approaches the rod separation. Use the Driven Wave Machine model to explore dispersion these effects.

The Wave Machine model 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. Other coupled oscillator models are available. They can be found by searching the OSP Collection for coupled oscillations.

References

"Standing waves in a non-uniform medium," Paul Gluck, The Physics Teacher, (in press).
"Making waves: A classroom torsional wave machine (Part I)," Kenneth D. Skeldon, Janet E. Milne, Alastair I. Grant, and David A. Palmer Phys. Teach. 36, 392 (1998)
"Making waves: A classroom torsional wave machine (Part II)," Kenneth D. Skeldon, Janet E. Milne, Alastair I. Grant, and David A. Palmer Phys. Teach. 36, 466 (1998)
University of Maryland Physics Lecture-Demonstration website section G3 http://www.physics.umd.edu/lecdem/services/demos/demosg3/demosg3.htm
Similarities in wave behavior, John N. Shive, Bell Telephone Laboratories (1961). See also Am. J. of Physics 32, p572 (1964).

Credits:

The Wave Machine model was created by Wolfgang Christian using the Easy Java Simulations (EJS) version 4.3 authoring and modeling tool created by Francisco Esquembre.

You can examine and modify this compiled EJS model if you run the model (double click on the model's jar file), right-click within a plot, and select "Open EJS Model" from the pop-up menu. You must, of course, have EJS installed on your computer. Information about EJS is available at: <http://www.um.es/fem/Ejs/> and in the OSP ComPADRE collection <http://www.compadre.org/OSP/>.

Translations

Code	Language		Translator	Run

Credits

Wolfgang Christian - Davidson College; Wee Loo Kang (weelookang@gmail.com); Felix J. Garcia Clemente

Briefing Document: 3D Wave Machine Simulation

1. Introduction

This document reviews the "3D Wave Machine JavaScript HTML5 Applet Simulation Model" developed by Wolfgang Christian and Loo Kang Wee, as hosted on the Open Educational Resources / Open Source Physics @ Singapore website. This interactive simulation models a physical wave machine originally created by John Shive at Bell Laboratories, allowing users to explore wave phenomena through a dynamic and customizable interface. The simulation is designed for educational purposes, allowing users to visualize and understand concepts related to wave propagation, reflection, and the factors that influence wave speed. It's available as a ready-to-run JavaScript version, and can be embedded on web pages.

2. Core Functionality and Design

Simulation of Physical Model: The applet simulates a wave machine consisting of horizontal bars attached to a torsion rod. As described in the source, "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 n horizontal bars with moment of inertia In welded to a torsion rod that is perpendicular to the bars."
Adjustable Parameters: Users can manipulate various parameters, including:
Bar Lengths (L1, L2): These can be changed to simulate waves in non-uniform media. The lengths are linked to moment of inertia where "The default bar of length L=2 has a moment of inertia of one. The maximum allowed bar length is 4 giving a moment of inertia of 4 and the minimum allowed length is 1/2 giving a moment of inertia of 1/16."
Torsional Spring Constant (k): Controls the coupling strength between bars, affecting wave speed.
Damping Coefficient (b): Simulates the effects of drag on the wave.
End Conditions: The far end of the wave machine can be set as either "Fixed End" or "Movable End," which influences the reflection of waves.
Mass (m): You can also add masses to the ends of the rods to see how inertia affects wave behavior.
Wave Generation: The simulation allows users to generate pulses or continuous waves by:
Twisting the first rod with the desired functional form. For instance, a "Gaussian twist produces a Gaussian traveling pulse."
Dragging the first rod to create a custom disturbance.
Visualization: The simulation offers a visual representation of wave motion, making abstract concepts more tangible for students. The source emphasizes the importance of this: "A wave is a disturbance that propagates through a medium, transferring energy. Water waves are familiar, but in science we extend the idea to other types of wave in other media."
Dispersion Effects: The simulation also subtly hints at wave dispersion, which is the phenomenon of wave shape distortion as it travels. As noted, "The pulse shape will distort as the wave propagates on the wave machine because of dispersion effects. This distortion is most apparent as the wavelength (or pulse width) approaches the rod separation." It suggests the "Driven Wave Machine model" for more in-depth exploration of dispersion.

3. Educational Applications and Learning Objectives

The simulation is intended to help students understand key concepts related to wave mechanics. Some of the teaching notes listed on the page include:

Basic Wave Principles: Demonstrates how a vibrating source sends a disturbance through a medium, transferring energy without the medium itself moving. "The basic principle of a wave: a vibrating source sends a disturbance through a medium. The wave travels, transferring energy, but the medium doesn’t move."
Reflection: Shows how waves reflect off a fixed end. "A wave reflects when it meets a fixed end."
Amplitude and Energy: Allows for exploration of the relationship between wave amplitude and energy. "Make bigger or smaller pulses – relate this to amplitude, and to energy, which is being transferred by the wave. Greater amplitude = greater energy."
Pulse Speed: Demonstrate that altering the disturbance length doesn't change the speed. "Make a faster disturbance – this makes a shorter pulse, but the speed is unchanged."
Continuous Waves: Show how continuous disturbances create continuous waves.
Wave Characteristics: Emphasizes the meaning of amplitude, wavelength, frequency, and wave speed. "Emphasise the meanings of amplitude, wavelength, frequency and wave speed."
Influence of Medium: Demonstrates how the wave speed is affected by the medium. "Frequency and amplitude depend on the source; speed and wavelength depend on the medium."
Relationship between Speed, Frequency and Wavelength: "Students could use the machine to investigate the relationship between wave speed, frequency and wavelength (speed = frequency ´ wavelength)."
Factors Affecting Wave Speed: Students can investigate how changes to the physical parameters (e.g. rod length, mass, spring constant) affect wave speed. For instance: "They could also change various factors and find out how wave speed changes: separation of the skewers, mass/number of jelly babies, position of jelly babies on skewers , width of tape , thickness of tape, etc."
Visual Analysis: Provides educators with a suggestion: "You could photograph the machine from the side to examine how the displacements of adjacent elements vary along the wave."

4. Implementation and Technical Details

Easy Java Simulations (EJS): The model was originally created using EJS, which is a tool for creating interactive simulations. As the source says: "The Wave Machine model was created by Wolfgang Christian using the Easy Java Simulations (EJS) version 4.3 authoring and modeling tool created by Francisco Esquembre."
JavaScript Version: The model has been converted to JavaScript, making it more accessible through web browsers. This version was created by Loo Kang Wee, who is credited alongside Wolfgang Christian in the Credits section.
Open Source: The simulation is part of an open educational resource and open source project, encouraging collaborative development and sharing. The site also states that "Contents are licensed Creative Commons Attribution-Share Alike 4.0 Singapore License ."
Physical Implementation: The website also includes practical advice on building a physical wave machine. "A wave machine is an entertaining way of introducing some basic ideas about wave motion." It goes on to list materials and construction advice, along with safety recommendations for educators.

5. Key Takeaways

The 3D Wave Machine simulation is a valuable tool for teaching wave mechanics, providing a dynamic and interactive way to visualize abstract concepts.
The simulation enables students to explore the relationship between various factors and wave behavior, promoting inquiry-based learning.
The JavaScript implementation makes it widely accessible for educational use.
The resource combines a virtual simulation with advice for a hands-on physical build, enriching the learning experience.
The simulation is based on a well-known physical model, making it relatable to classic wave demonstrations.

6. Supporting Resources

The document also provides links to several articles on similar wave machines, along with references to the software used to create the simulation. Here's a sample of the resources included:

References to articles: "Making waves: A classroom torsional wave machine" (Part I and II) and "Standing waves in a non-uniform medium"
Links to similar wave machine demonstrations, including one by the National STEM Centre
Links to the EJS website

7. Conclusion

The 3D Wave Machine simulation is a powerful tool for teaching wave phenomena in an engaging and interactive way. Its customizable parameters, combined with clear visual representation, make it a valuable resource for educators. By combining the simulation with the hands-on building instructions provided, teachers can also facilitate a hands on approach in student learning.

Wave Machine Study Guide

Short Answer Quiz

What is the purpose of the Wave Machine model, and what real-world apparatus does it simulate?
Describe how the wave machine is constructed and how its components interact to create a wave.
Explain how the simulation allows users to manipulate the characteristics of the wave machine, and what effects these adjustments have.
What role does the torsional coupling (k) play in wave propagation on the machine?
How does damping (b) affect the waves in the simulation?
What happens when you apply a Gaussian twist to the first rod in the simulation?
How do the fixed and free end conditions change the way waves are reflected in the simulation?
According to the "Theoretical note" in the source, what causes the pulse shape to distort as the wave propagates?
List three key wave characteristics that can be explored using the simulation and briefly explain what those terms mean.
Explain one way the simulation can be used as a teaching tool.

Short Answer Quiz - Answer Key

The Wave Machine model simulates a physical wave machine made famous by the PSSC Simple Waves film, allowing users to visualize and interact with wave behavior. The model is used to explore how waves travel through a medium and how various factors impact wave behavior.
The wave machine consists of horizontal bars attached to a torsion rod. Twisting one bar causes it to oscillate, and the motion is transferred to neighboring bars through the torsion rod resulting in a travelling wave.
Users can change the lengths of the bars, simulate a non-uniform medium, apply different initial pulse shapes, and select fixed or free ends of the wave machine. These changes will affect wave speed, pulse shape, and reflection behavior.
The torsional coupling constant (k) determines the strength of the restoring torque between adjacent bars. Higher values of 'k' result in a stronger restoring force and potentially faster wave speeds.
Damping (b) adds a drag force to the system, which causes the amplitude of the waves to decrease over time, simulating energy dissipation in a real-world medium.
Applying a Gaussian twist to the first rod produces a Gaussian traveling pulse down the machine. The width of the pulse will depend on the wave speed in the medium.
A fixed end will reflect the wave with a 180-degree phase shift (inversion) while a free end reflects the wave without a phase shift.
The pulse shape distorts because of dispersion effects. This distortion is most apparent when the pulse width approaches the rod separation.
Three key characteristics are amplitude, the maximum displacement from equilibrium; wavelength, the distance between two successive crests or troughs; and frequency, how often the wave oscillates at a given point.
The simulation can be used to demonstrate fundamental wave properties (e.g. reflection, energy transfer, amplitude, wavelength, frequency), or to test the relationship between wave speed, frequency, and wavelength.

Essay Questions

Discuss how the Wave Machine simulation can be used to model real-world scenarios involving wave propagation in different media. In your answer, consider the impact of the various parameters available for adjustment in the model.
Analyze the educational value of using simulations like the Wave Machine model in teaching physics concepts related to waves. Consider how interactive models can enhance learning.
Explain the concept of wave dispersion in the context of the Wave Machine simulation. Describe how dispersion affects the shape of the wave pulse and why it occurs.
Compare and contrast the behavior of waves when they encounter a fixed end versus a free end in the simulation. Discuss the physics principles behind the different reflections.
Describe the process of creating a physical wave machine, including the materials needed and the assembly. Discuss how it can be used in tandem with the digital simulation and what insights that could provide.

Glossary

Wave Machine: A device or simulation that demonstrates wave propagation, typically consisting of coupled oscillating elements.
Torsional Rod: A rod designed to twist and exert a restoring torque when twisted. In the wave machine, this rod connects the horizontal bars.
Moment of Inertia: A measure of an object's resistance to changes in its rotational motion. In the context of the wave machine, it applies to the horizontal bars.
Torsional Coupling (k): A measure of how strongly neighboring bars are connected by the torsion rod. It affects the restoring force and the wave speed.
Damping (b): A force that opposes motion and dissipates energy from the system, causing the wave amplitude to decrease over time.
Gaussian Pulse: A pulse shape characterized by a bell-shaped curve, often used in simulations to model localized disturbances.
Fixed End: A boundary condition in the simulation where the end of the wave machine is constrained and cannot move. It leads to a reflected wave with a 180-degree phase shift.
Free End: A boundary condition where the end of the wave machine is free to move, resulting in a reflected wave without a phase shift.
Dispersion: A phenomenon where the speed of a wave depends on its frequency or wavelength, leading to the distortion of a pulse as it travels.
Amplitude: The maximum displacement of a wave from its equilibrium position; relates to the energy carried by the wave.
Wavelength: The distance between two successive crests or troughs of a wave; represents one complete cycle of the wave.
Frequency: The number of oscillations or cycles of a wave that occur in a unit of time, usually a second; indicates how rapidly the wave is oscillating.
Pulse: A single disturbance or wave packet that travels through a medium.

For Teachers

Legends of symbols used

Fixed End , means the far end of the wave machine is fixed, possibly for exploring reflecting wave formation etc.

Movable End, means the far end of the wave machine is it movable, like a ring on a sliding rod etc

A = Amplitude of Wave in Angle from centre of the rod, so A = 0 means no amplitude, A = π/2 is a 90 degree turn of the first rod on the wave machine

m = mass attached to the ends of the rods, to allow inquiry into the effects of adding extra point masses on the ends of the rods

L1 = near end of the wave machine variable from 2 to 4 m for inquiry into effects of length of rods and the effects of higher inertia to rotation.

L2 = far end of the wave machine variable from 2 to 4 m for inquiry into effects of length of rods and the effects of higher inertia to rotation.

k = torsional spring constant of the rope attaching to all the rods, low k means restoring moment lesser, high k means restoring moments higher

b = drag coefficient in a high viscous medium of air etc, to show effects of air drag

Teaching notes

1 As with the ripple tank, it helps if you start by demonstrating single pulses before going on to continuous waves. Deflect a section of the machine close to the end or you will get pulses running in opposite directions. Try to avoid setting up standing waves which can be confusing.
Show that a pulse/disturbance travels along the line. Point out that the mass (jelly babies) are displaced up and down (vertically) while the wave travels along horizontally.

2 You can demonstrate the following:

The basic principle of a wave: a vibrating source sends a disturbance through a medium. The wave travels, transferring energy, but the medium doesn’t move.
A wave reflects when it meets a fixed end.
Make bigger or smaller pulses – relate this to amplitude, and to energy, which is being transferred by the wave. Greater amplitude = greater energy.
Make a faster disturbance – this makes a shorter pulse, but the speed is unchanged.
Show that continuous disturbance by the source results in continuous waves.
Emphasise the meanings of amplitude, wavelength, frequency and wave speed.
Frequency and amplitude depend on the source; speed and wavelength depend on the medium.

3 You can adapt the machine to show that the speed of a wave changes when it moves into a different medium by adding or removing mass. A stopwatch is adequate for timing a wave to deduce its speed, but note that waves travel very quickly along a machine which has no jelly babies on its skewers.

4 Students could use the machine to investigate the relationship between wave speed, frequency and wavelength (speed = frequency ´ wavelength). They could also change various factors and find out how wave speed changes: separation of the skewers, mass/number of jelly babies, position of jelly babies on skewers, width of tape, thickness of tape, etc.
5 You could photograph the machine from the side to examine how the displacements of adjacent elements vary along the wave.

Big Picture

A wave is a disturbance that propagates through a medium, transferring energy. Water waves are familiar, but in science we extend the idea to other types of wave in other media.
A wave can only travel if the elements of the medium are connected in some way; in this case, each rod affects the next by twisting the tape that connects them.

Waves are characterised by their amplitude and frequency (determined by the source) and their speed (determined by the medium). The wavelength depends on the frequency and the speed.

Wave Machine

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 n horizontal bars with moment of inertia In 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 default bar of length L=2 has a moment of inertia of one. The maximum allowed bar length is 4 giving a moment of inertia of 4 and the minimum allowed length is 1/2 giving a moment of inertia of 1/16. Twisting a bar about the torsion rod causes the bar to oscillate because the rod produces a restoring torque. Because a bar twist acts on neighboring bars, the motions are coupled and a traveling wave results. The speed of the wave depends on the torsional coupling between bars k and the moments of inertia of the bars. A damping force can also be added using the model's damping parameter b.

Theoretical note: The pulse shape will distort as the wave propagates on the wave machine because of dispersion effects. This distortion is most apparent as the wavelength (or pulse width) approaches the rod separation. Use the Driven Wave Machine model to explore dispersion these effects.

The Wave Machine model is distributed as a ready-to-run (compiled) Java archive but now available as JavaScript version.

Demonstration and Building a Physical Demo wave machine

A wave machine is an entertaining way of introducing some basic ideas about wave motion.

Apparatus and material

For the demonstration

Duct tape
Clamps and stands, G clamps
Barbecue skewers
Jelly babies (jelly beans)
Metre rule
Stopwatch or stop clock

A 5 m wave machine will require about 100 skewers and 200 jelly babies.

Commercially-manufactured wave machines are available, but the attraction of this home-made version is that its construction and mechanism are clear to students.

Health & Safety and Technical notes

Students should be advised to take care when handling pointed skewers. They should be instructed not to eat the jelly babies, which should be disposed of safely after use (the jelly babies, not the students

Video

Wave Machine Demonstration by National STEM Centre

References

- "Standing waves in a non-uniform medium," Paul Gluck, The Physics Teacher, (in press).
- "Making waves: A classroom torsional wave machine (Part I)," Kenneth D. Skeldon, Janet E. Milne, Alastair I. Grant, and David A. Palmer Phys. Teach. 36, 392 (1998)
- "Making waves: A classroom torsional wave machine (Part II)," Kenneth D. Skeldon, Janet E. Milne, Alastair I. Grant, and David A. Palmer Phys. Teach. 36, 466 (1998)
- University of Maryland Physics Lecture-Demonstration website section G3 http://www.physics.umd.edu/lecdem/services/demos/demosg3/demosg3.htm
- Similarities in wave behavior, John N. Shive, Bell Telephone Laboratories (1961). See also Am. J. of Physics 32, p572 (1964).
Credits:

The Wave Machine model was created by Wolfgang Christian and Loo Kang Wee (JavaScript version) using the Easy Java Simulations (EJS) version 4.3 authoring and modeling tool created by Francisco Esquembre and Felix J. Garcia Clemente.

You must, of course, have EJS downloaded and open before on your computer. Information about EJS is available at: <http://www.um.es/fem/Ejs/> and in the OSP ComPADRE collection <http://www.compadre.org/OSP/>.

Reference:

FAQ

What is a wave machine and how does it work? A wave machine is a device designed to visually demonstrate wave motion. It typically consists of a series of horizontal bars connected to a torsion rod. When one bar is twisted, it causes its neighbors to twist due to the torsional coupling between them, resulting in a wave traveling down the machine. The restoring torque from the torsion rod causes the bars to oscillate, which drives the wave's motion. The speed of the wave depends on the coupling between the bars and their moment of inertia, which is related to their length and mass.
What factors affect the speed of a wave on a wave machine? The speed of a wave on a wave machine is influenced by several factors. Primarily, it is determined by the torsional coupling strength between the bars (represented by k), and the moments of inertia of the bars themselves. The length and mass distribution of the bars directly affect their moments of inertia. A stiffer connection (higher k) or lower moment of inertia results in a faster wave speed. The medium also plays a role where a wave is also affected by the damping force of air via parameter b.
Can the wave machine demonstrate different types of wave behavior? Yes, the wave machine can demonstrate various wave behaviors. It shows how a pulse travels, reflects when it meets a fixed end, and changes direction or amplitude at a movable end. You can change amplitude and frequency of the disturbance, as well as add mass to the rods to show how the wave speed changes. It's useful for understanding concepts like amplitude, wavelength, frequency, and wave speed. Continuous disturbance results in a continuous wave.
What is the significance of the "fixed end" versus "movable end" settings on the wave machine? The "fixed end" setting simulates a situation where the end of the wave machine cannot move. In this case, when a wave reaches the end, it reflects back with an inversion. The "movable end" allows the end of the wave machine to move freely, which also reflects the wave but without inversion. These settings demonstrate how the boundary conditions impact wave reflection. This is applicable to physics in understanding reflections in many areas of wave theory.
Why would one use a wave machine simulation instead of a real wave machine? A wave machine simulation, such as the JavaScript applet described, provides several advantages. It is convenient, easily accessible on computers, and allows users to manipulate parameters such as bar length, damping, and coupling to explore wave behavior under various conditions. It allows for precise control of the initial pulse and end conditions, providing controlled environments for learning. Real wave machines are educational and tangible, but simulations complement that learning process with further investigation of variables in a controllable environment.
What is meant by 'dispersion effects' in the context of the wave machine? Dispersion effects refer to the distortion of a wave pulse as it propagates. This occurs because the speed of a wave depends on its frequency, or in this case, pulse width relative to the rod separation, and thus different frequency components of a complex wave pulse travel at different speeds. As a result, the pulse changes shape as it moves. The distortion becomes more significant when the wavelength or pulse width is comparable to the separation between the rods in the wave machine.
How can a wave machine be used to teach basic concepts of waves? Wave machines are excellent tools for introducing fundamental wave concepts. They visually demonstrate that a wave is a disturbance moving through a medium, transferring energy, but the medium itself doesn't move. They illustrate amplitude, wavelength, frequency, and wave speed, and how these are related. They can be used to show reflection, superposition and other wave phenomena, and can provide direct experience with how the medium properties affect wave behavior. Students can use wave machines to investigate the relationship between wave speed, frequency, and wavelength, for example.
Besides the traditional physical wave machine, what modern tools are available to simulate wave behavior? Besides physical wave machines, modern educational tools include interactive simulations like JavaScript-based applets (such as the one mentioned). These simulations provide user interfaces to directly manipulate parameters and visualize waves in controlled environments. They help illustrate concepts that might be hard to observe in physical setups and enable students to study dispersion, reflection at boundaries, and effects of medium property changes.

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Details: Written by Fremont; Parent Category: 03 Waves; Category: 01 General Waves; Published: 30 April 2018; Created: 30 April 2018; Last Updated: 02 February 2025; Hits: 13390

General Waves

Breadcrumbs

🌊3D Wave Machine JavaScript HTML5 Applet Simulation Model by Wolfgang Christian and Loo Kang WEE

About

Wave Machine

References

Credits:

Translations

Credits

Wave Machine Study Guide

Short Answer Quiz

Short Answer Quiz - Answer Key

Essay Questions

Glossary

For Teachers

Teaching notes

Wave Machine

Demonstration and Building a Physical Demo wave machine

Video

References

Credits:

Reference:

FAQ