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written by
Kyle Forinash and
Wolfgang Christian
This is a collection of interactive tutorials on the fundamentals of waves. The tutorials emphasize concepts that are not usually easy to illustrate in textbooks. Java applets are used to illustrate the physics. The lessons begin with very simple wave properties and end with an examination of nonlinear wave behavior.
Ready-to-run examples (33)
1. Introduction to Waves Tutorial
Waves: An Interactive Tutorial is a set of 33 exercises designed to teach the
2. Sine Wave
This simulation shows a perfect, smooth wave out on the ocean far enough from shore so that it has not started to break (complications involved in describing real waves will be discussed later in this tutorial).
3. Speed of a Wave
There are three different velocities involved with describing a wave, one of which will be introduced in this simulation.
4. Transverse Waves
This simulation shows the motion of a wave that is up and down so that as the wave moves forward the material moves perpendicular (or transverse) to the direction the wave moves.
5. Simple Harmonic Motion
This simulation shows a mass on a spring and graphs the position time dependence.
7. Longitudinal Waves
This simulation shows waves where the motion of the material is back and forth in the same direction that the wave moves. Sound waves (in air and in solids) are examples of longitudinal waves.
8 Water Waves
Waver Waves, like many real physical waves, are combinations of three kinds of wave motion; transverse, longitudinal and torsional.
9. Two-Dimensional Waves
This simulation shows a plane wave in two dimensions traveling in the x-y plane, in the x direction, viewed from above. In these simulations the amplitude (in the z direction, towards you) is represented in grey-scale.
10. Adding Two Linear Waves (Superposition)
This simulation shows the sum of two wave functions u(x,t) = f(x,t) + g(x,t).
11. Interference
This simulation shows a top view of a source making waves on the surface of a tank of water. The white circles coming from the spot represents the wave crests with troughs in between. Two sources can be seen at the same time and the separation between them and the wavelength of both can be adjusted
12. Group Velocity
The Group Velocity simulation shows how several waves add together to form a single wave shape.
13. Other Wave Functions
This simulation explores how any function of x and t which has these variables in the form x - v t will be a traveling wave with speed v.
14. Fourier Analysis and Synthesis
This simulation demonstrates Fourier analysis and synthesis. Fourier analysis is the process of mathematically breaking down a complex wave into a sum of of sines and cosines. Fourier synthesis is the process of building a particular wave shape by adding sines and cosines.
15. Mirrors
This simulation exploration of specular reflection fro plane, concave, and convex surfaces.
16. Collisions with Boundaries
This simulation shows how the phase of the wave may be different after reflection, depending on the surface from which they reflect.
17. Standing Waves on a String
This simulation shows how a standing wave on a string is formed from two identical waves moving in opposite directions.
18. Refraction
This simulation shows how a wave that changes speed as it crosses the boundary of between two materials will also change direction if it crosses the boundary at an angle other than perpendicular.
19. Lenses
The simulation shows how light is bent by a lens using the thin lens approximation which assumes the lens thickness is small compared to the curvature of the glass.
20. Path Difference and Interference
This simulation shows two identical waves that start at different locations. A third graph shows the sum of these two waves.
21. Impedance
This simulations models a string as a row of individual masses connected by invisible springs. Waves are reflected in the middle of this string because the mass of the string is different on the left as compared with the right.
22. Dispersion of Light
This simulation shows visible light passing through a prism. You can choose the color and see what the index is for that wavelength.
23. Dispersion of Fourier Components
This simulation starts with the first four components of the Fourier series for a traveling square wave with no dispersion. Changing the angular frequency of a component causes the initial wave function to distort due to dispersion.
24. Diffraction
This simulation shows what happens to a plane-wave light source (below the simulation, not shown) as it passes through an opening. The wavelength of the waves and the size of the opening can be adjusted.
25. Doppler Effect
This simulation models at the Doppler effect for sound; the black circle is the source and the red circle is the receiver. If either the source or the receiver of a wave are in motion the apparent wavelength and frequency of the received wave change. This is apparent shift in frequency of a moving source or observer is called the Doppler Effect. The speed of the wave is not affected by the motion of the source or receiver and neither is the amplitude.
26. EM Waves from an Accelerating Charge
This simulation shows an accelerating positive charge and the electric field around it in two dimensions. Because the charge is accelerated there will be a disturbance in the field. The energy carried by the disturbance comes from the input energy needed to accelerate the charge.
27. Antenna
This simulation shows the effect of a wave traveling in the x-direction on a second charge inside a receiving antenna. Only the y-component of the change in the electric field is shown (so an oscillation frequency of zero will show nothing, because there is only a constant electric field).
28. Electromagnetic Plane Waves
This simulation shows a plane electromagnetic wave traveling in the y-direction. Both electric and magnetic fields are shown in the 3D representation.
29. Polarization
This simulation shows the electric field component[s] for a wave traveling straight towards the observer in the +y direction. A polarized wave was previously defined to be an electromagnetic wave that has its electric field confined to change in only one direction. In this simulation we further investigate polarized waves.
30. Wave Equation
In this simulation we look at the dynamics of waves; the physical situations and laws give rise to waves. We start with a string that has a standing wave on it and look at the forces acting on each end of a small segment of the string due to the neighboring sections. For visualization purposes the string is shown as a series of masses but the physical system is a continuous string. Although the derivation is for a string, similar results occur in many other systems.
31. Oscillator Chain
In this simulation we examine waves that occur on chains of masses with mass M coupled together with elastic, Hooke's law forces (F = -?x where ? is the spring constant and x is the amount the spring stretches). The masses are constrained to only move up and down so that the stretching depends only on the difference in the y locations of the masses.
32. Non-Linear Waves
This simulations shows what happens if forces other than tension act on a string. Some additional forces cause the dispersion we saw in simulations 22 and 23 but friction, dissipation and nonlinearity can cause other behavior as we will see here.
33 Solitons
This simulation explores a special solution of the non-linear wave equation where the effects of dispersion and dissipation (which tend to make a wave pulse spread out) are exactly compensated for by a nonlinear force (which, as we have seen, tends to cause steepening of a wave). In this case there may be a special wave pulse shape that can travel and maintain its shape called a soliton.
View the supplemental documents attached to this resource (33)
Introduction to Waves Tutorial
Waves: An Interactive Tutorial is a set of 33 exercises designed to teach the fundamentals of wave dynamics. It starts with very simple wave properties and… more... download 241kb .zip Last Modified: July 28, 2015
Sine Waves
This simulation shows a perfect, smooth wave out on the ocean far enough from shore so that it has not started to break (complications involved in describing… more... download 115kb .zip Rights: Creative Commons Attribution-Noncommercial-Share Alike 3.0. Last Modified: May 30, 2015 previous versions
Speed of a Wave
There are three different velocities involved with describing a wave, one of which will be introduced in this simulation. download 125kb .zip Last Modified: May 30, 2015 previous versions
Transverse Waves
Transverse waves are the kind of wave you usually think of when you think of a wave. The motion of the material constituting the wave is up and down so that… more... download 144kb .zip Rights: Creative Commons Attribution-Noncommercial-Share Alike 3.0. Last Modified: May 30, 2015 previous versions
Simple Harmonic Motion
The Simple Harmonic Motion simulation shows the motion a mass on a spring graphs its time dependence. download 138kb .zip Rights: Creative Commons Attribution-Noncommercial-Share Alike 3.0. Last Modified: May 30, 2015 previous versions
Simple Harmonic Motion and Resonance
The Simple Harmonic Motion and Resonance simulation shows a driven damped harmonic oscillator. The user can select under damped, over damped, and critically… more... download 140kb .zip Rights: Creative Commons Attribution-Noncommercial-Share Alike 3.0. Last Modified: May 30, 2015 previous versions
Longitudinal Waves
The Longitudinal Waves simulation shows waves where the motion of the material is back and forth in the same direction that the wave moves. Sound waves (in… more... download 138kb .zip Rights: Creative Commons Attribution-Noncommercial-Share Alike 3.0. Last Modified: May 30, 2015 previous versions
Waves Waves
Waver Waves, like many real physical waves, are combinations of three kinds of wave motion; transverse, longitudinal and torsional. download 125kb .zip Rights: Creative Commons Attribution-Noncommercial-Share Alike 3.0. Last Modified: May 30, 2015 previous versions
Two-Dimensional Waves
The Two-Dimensional Waves simulation shows a plane wave in two dimensions traveling in the x-y plane, in the x direction, viewed from above. In these… more... download 125kb .zip Rights: Creative Commons Attribution-Noncommercial-Share Alike 3.0. Last Modified: May 30, 2015 previous versions
Adding Linear Waves (Superposition)
Linear waves have the property, called superposition, that their amplitudes add linearly if they arrive at the same point at the same time. This simulation… more... download 113kb .zip Rights: Creative Commons Attribution-Noncommercial-Share Alike 3.0. Last Modified: May 30, 2015 previous versions
Interference
The Interference simulation shows a top view of a source making waves on the surface of a tank of water (imagine tapping the surface of a pond with the end… more... download 127kb .zip Rights: Creative Commons Attribution-Noncommercial-Share Alike 3.0. Last Modified: May 30, 2015 previous versions
Group Velocity
The Group Velocity simulation shows how several waves add together to form a single wave shape (called the envelope) and how we can quantify the speed with… more... download 145kb .zip Rights: Creative Commons Attribution-Noncommercial-Share Alike 3.0. Last Modified: May 30, 2015 previous versions
Other Wave Functions
The Other Wave Functions simulation explores how any function of x and t which has these variables in the form x - v t will be a traveling wave with speed v. download 107kb .zip Rights: Creative Commons Attribution-Noncommercial-Share Alike 3.0. Last Modified: May 30, 2015 previous versions
Fourier Analysis and Synthesis
Fourier analysis is the process of mathematically breaking down a complex wave into a sum of of sines and cosines. Fourier synthesis is the process of… more... download 947kb .zip Last Modified: May 30, 2015
Mirrors
The Mirrors simulation exploration of specular reflection fro plane, concave, and convex surfaces. download 135kb .zip Rights: Creative Commons Attribution-Noncommercial-Share Alike 3.0. Last Modified: May 30, 2015 previous versions
Collisions with Boundaries
The Collisions with Boundaries simulation shows how the phase of the wave may be different after reflection, depending on the surface from which they reflect. download 127kb .zip Rights: Creative Commons Attribution-Noncommercial-Share Alike 3.0. Last Modified: May 30, 2015 previous versions
Standing Waves
This simulation shows how a standing wave is formed from two identical waves moving in opposite directions. For standing waves on a string the ends are fixed… more... download 128kb .zip Last Modified: May 30, 2015
Refraction
This simulation shows how a wave that changes speed as it crosses the boundary of between two materials will also change direction if it crosses the boundary… more... download 109kb .zip Last Modified: May 30, 2015
Lenses
This simulation shows how light rays are bent using the thin lens approximation which assumes the lens thickness is small compared to the curvature of the… more... download 119kb .zip Last Modified: May 30, 2015
Path Difference and Interference
This simulation shows two identical waves that start at different locations. A third graph shows the sum of these two waves. download 113kb .zip Last Modified: May 30, 2015
Impedance
This simulations represents a string as a row of individual masses connected by invisible springs. Waves are reflected in the middle of this string because… more... download 1809kb .zip Last Modified: May 30, 2015
Dispersion of Light
This simulation shows visible light passing through a prism. You can choose the color and see what the index is for that wavelength. download 111kb .zip Last Modified: May 31, 2015
Dispersion of Fourier Components
This simulation starts with the first four components of the Fourier series for a traveling square wave with no dispersion. Changing the angular frequency of… more... download 114kb .zip Last Modified: May 31, 2015
Diffraction
This simulation shows what happens to a plane-wave light source (below the simulation, not shown) as it passes through an opening. The wavelength of the… more... download 119kb .zip Last Modified: May 31, 2015
Doppler Effect
This simulation models at the Doppler effect for sound; the black circle is the source and the red circle is the receiver. If either the source or the… more... download 124kb .zip Last Modified: May 31, 2015
EM Waves from an Accelerating Charge
This simulation shows an accelerating positive charge and the electric field around it in two dimensions. Because the charge is accelerated there will be a… more... download 129kb .zip Last Modified: May 31, 2015
Antenna
This simulation shows the effect of a wave traveling in the x-direction on a second charge inside a receiving antenna. Only the y-component of the change in… more... download 106kb .zip Last Modified: May 31, 2015
Electromagnetic Plane Waves
This simulation shows a plane electromagnetic wave traveling in the y-direction. Both electric and magnetic fields are shown in the 3D representation. download 131kb .zip Last Modified: May 31, 2015
Polarization
This simulation shows the electric field component[s] for a wave traveling straight towards the observer in the +y direction. A polarized wave was previously… more... download 121kb .zip Last Modified: May 31, 2015
Wave Equation
In this simulation we look at the dynamics of waves; the physical situations and laws give rise to waves. We start with a string that has a standing wave on… more... download 224kb .zip Last Modified: June 29, 2015
Oscillator Chain
In this simulation we examine waves that occur on chains of masses with mass M coupled together with elastic, Hooke's law forces (F = -?x where ? is the… more... download 219kb .zip Rights: Creative Commons Attribution-Noncommercial-Share Alike 3.0. Last Modified: July 25, 2015
Non-Linear Waves
This simulations shows what happens if forces other than tension act on a string. Some additional forces cause the dispersion we saw in simulations 22 and 23… more... download 207kb .zip Last Modified: July 29, 2015 previous versions
Solitons
This simulation explores a special solution of the non-linear wave equation where the effects of dispersion and dissipation (which tend to make a wave pulse… more... download 205kb .zip Last Modified: July 29, 2015
View the source code documents attached to this resource (2)
Sine Waves Source Code
This source code zip archive contains an XML representation of the Sine Wave JavaScript Model. Unzip this archive in your Ejs workspace to compile and run… more... download 37kb .zip Last Modified: March 20, 2015 previous versions
Speed of a Wave Source Code
This source code zip archive contains an XML representation of the Speed of a Wave JavaScript Model. Unzip this archive in your Ejs workspace to compile and… more... download 46kb .zip Last Modified: March 20, 2015 previous versions
will all the src be available for download?
Author: lookang it appears only Sine Waves Source Code and Speed of a Wave Source Code are visible.
» reply
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Common Core State Standards for Mathematics AlignmentsHigh School — Algebra (9-12)
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<a href="http://www.compadre.org/psrc/items/detail.cfm?ID=3146">Forinash, Kyle, and Wolfgang Christian. Waves: An Interactive Tutorial. August 9, 2005.</a>
AIP Format
K. Forinash and W. Christian, (2002), WWW Document, (http://pages.iu.edu/~kforinas/WJS/WavesJS.html).
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K. Forinash and W. Christian, Waves: An Interactive Tutorial, (2002), <http://pages.iu.edu/~kforinas/WJS/WavesJS.html>.
APA Format
Forinash, K., & Christian, W. (2005, August 9). Waves: An Interactive Tutorial. Retrieved August 31, 2015, from http://pages.iu.edu/~kforinas/WJS/WavesJS.html
Chicago Format
Forinash, Kyle, and Wolfgang Christian. Waves: An Interactive Tutorial. August 9, 2005. http://pages.iu.edu/~kforinas/WJS/WavesJS.html (accessed 31 August 2015).
MLA Format
Forinash, Kyle, and Wolfgang Christian. Waves: An Interactive Tutorial. 2002. 9 Aug. 2005. 31 Aug. 2015 <http://pages.iu.edu/~kforinas/WJS/WavesJS.html>.
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@misc{
Author = "Kyle Forinash and Wolfgang Christian",
Title = {Waves: An Interactive Tutorial},
Volume = {2015},
Number = {31 August 2015},
Month = {August 9, 2005},
Year = {2002}
}
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%A Kyle Forinash
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