Acoustics and Vibration Animations
Professor of Acoustics
Director of Distance Education
Graduate Program in Acoustics
The links below contain animations illustrating acoustics and vibration, waves and oscillation concepts. I started using Mathematica to create animations to help me understand and visualize certain acoustics and vibration phenomena in 1992 while I was a Ph.D. student in the Graduate Program in Acoustics at Penn State. For the next 16 years (1995-2011) I was a physics professor at Kettering University and continued creating animations and using them as educational tools for the courses I was teaching about waves and acoustics. Sometime around 1998 or so I began writing webpages and adding them to this online collection. Now that I'm back at Penn State, teaching graduate level acoustics, I'm continuing to add to my collection of animations. My intent has always been to create physically and mathematically correct animations, accompanied by explanatory text, that illustrate complicated phenomena involving waves and vibration in a manner that aids student understanding. I hope you find these animations useful.
This work by Dan Russell is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Based on a work at http://www.acs.psu.edu/drussell/demos.html. Additional information about using this content is available at http://www.acs.psu.edu/drussell/Demos/copyright.html.
Today is . The contents (and links) on this page were last updated on February 18, 2014.
I am in the process of attempting to bring all of the pages on this site into compliance with current HTML5, CSS3, and W3C Web Accessibility standards. The bullet symbols used in the lists below identify pages as
- (open circle) still needs to be updated
- (filled disc) updated to HTML5 and CSS3.
As far as I can tell most of the updated pages work correctly with Firefox v.41, Safari v8 (but NOT with Safari 9.0), Google Chrome v24, Maxthon 4, and Explorer v10. I am trying to figure out and fix the style problems with Safari 9. Many of the pages below include math equations formatted using MathML, and I have learned that Chrome versions after 24 have removed support for MathML, and Internet Explorer requires the MathPlayer plugin in order to render MathML equations properly.
Please let me know if you find page errors or pages that don't load correctly. Thanks!
Sound Waves and Sources
Basic Wave Phenomena
Sound Waves and Radiation from Sources
More Complicated Wave Phenomena
Vibration and Structural Waves
Vibration of 1-DOF Simple Oscillators
Vibration of Multi-DOF Systems
Vibrational Modes of Continuous Systems
Interactive Plots Demonstrating Acoustic Phenomena
The interactive plots in these links contain Mathematica Computable Document Format files and require the use of the free Wolfram CDF Player.
Tools used to create these animations
- Mathematica -- Almost all of the animations, and all of the interactive CDF plots, were conceived and created with Mathematica. This ensures that the animations are physically and mathematically correct instead of being cutesy cartoons.
- COMSOL Multiphysics -- there are a few animations on some of the newer pages that involve problems without nice analytical solutions, but which instead require computational (finite element or boundary element) solutions. I have started using COMSOL Multiphysics to numerically model these problems and to create a few animations.
- GIFfun -- While I design and create the animations with Mathematica, the actual animated GIF images on my webpages have been created with GIFfun from Stone Design.