• Except where otherwise noted, all animations were created by myself using Mathematica.
• Please send comments about this page to: drussell@egnr.psu.edu

Copyright Questions and Permissable Use of Animations

Today is The contents (and links) on this page were last updated on January 24, 2012.

Newest Animations:

• Vibrational Modes of a Tuning Fork. (added 01/24/2012) - how does a tuning fork vibrate?
• Reflections from Impedance and the Standing Wave Ratio. (added 10/08/2011) - A sinusoidal wave train reflects from an impedance discontinuity. The resulting wave pattern defines the Standing Wave Ratio used to measure impedance.

Basic Wave Phenomena

• What is a Wave? - a disturbance which travels through a medium
• Wave Motion in Space and Time - distinguishing between the time behavior and spatial behavior of waves
• Superposition of Two Waves - Interference, Standing Waves, and Beats (Updated: 10/26/2011)
• Fourier Decomposition - building a wave shape from sines and cosines [no text yet , but movies work]
• Phase changes upon reflection from hard, soft, and mixed boundaries
• Reflections from Impedance and the Standing Wave Ratio. (added 10/08/2011) - A sinusoidal wave train reflects from an impedance discontinuity. The resulting wave pattern defines the Standing Wave Ratio used to measure impedance.
• Refraction of Sound Waves - how temperature gradients make sound waves change direction
• The Doppler Effect - moving sound sources and sonic booms

Sound Waves and Radiation from Sources

• Longitudinal and Transverse Waves - Particle Motion for Longitudinal, Transverse, Water and Rayleigh Surface Waves
• Sound Fields Radiated by Simple Sources - pressure sound fields produced by monopole, dipole, and quadrupole sources
• Sound Radiation from Cylindrical Radiators - particle motion and sound fields produced by vibrational modes of a cylinder
• Sound field radiated by a Tuning Fork - animations to accompany a paper submitted to the American Journal of Physics
• The Baffled Piston - approximation of the sound field radiated by a loudspeaker

More Complicated Wave Phenomena

• Evanescent Modes in Waveguides - higher order modes in ducts driven above and below their cutoff frequency.
• Waves in Dispersive Media - when wave speed depends on frequency
• Examples of Dispersive Waves --- Flexural waves and Quasi-longitudinal waves on a rod
• Collision Between Two Solitary Waves - what is a soliton? and what happens when two solitons collide?

Room Acoustics

• Driving room modes & source location - How does the (resonance) response of a room depend on source location?
• Reverberation Times in a small room - sound files and plots for measurements of T₆₀.

Vibration of 1-DOF Simple Oscillators

• Comparing Circular and Sinusoidal Motion - how is circular motion in the complex plane (magnitude and phase) related to sine and cosine functions?
• Simple Harmonic Oscillator - with and without damping, transfer of energy between kinetic and potential forms
• Damped Harmonic Oscillator - underdamped, overdamped, and critically damped
• Phase-Space Diagrams for an Oscillator - plotting velocity v(t) as a function of position x(t)
• Forced Harmonic Oscillator - transient and steady state response to a force applied to the mass
• Base Motion - transient and steady state response of an oscillator to displacement of its support
• The Simple Pendulum - comparing the linear approximation (small angle) with a real pendulum

Vibration of Multi-DOF Systems

• Coupled Oscillators - energy transfer between two mass-spring systems coupled together
• Dynamic Absorbers - J.P. Den Hartog's classical undamped tuned dynamic absorber
• Vibrational modes of a multi-dof system - progression of mode shapes from single degree-of-freedom to continuous structure
• Multiple-DOF mass-spring systems. (added 9/20/2011) - improved animation of the natural modes of a multi-degree-of-freedom mass-spring system.

Vibrational Modes of Continuous Systems

• Vibrational Modes of a Hanging Chain - mode shapes for a hanging chain
• Vibration of a Fixed-Fixed String - mode shapes, and frequency spectra for a plucked string
• Rectangular Membrane - and degenerate modes of a square membrane [no text yet, but movies work]
• Circular Membrane - or how a drum head vibrates
• Flexural Vibrations of a Beam - how the mode shapes depend on boundary conditions (no text yet, but animations work)
• Vibrational Modes of a Tuning Fork. (added 01/24/2012) - how does a tuning fork vibrate?
• Vibration of Baseball Bats - bending modes (sweet spot) and cylinder modes (ping)
• Bending and Torsional Vibration in a Hockey Stick - flexural bending and torsional twisting vibration in a hockey stick
• Vibration Modes of a Glass Beer Bottle - what vibration shapes are responsible for the "clink" of a glass bear bottle?
• Vibrational Modes of an Electric Guitar - actual experimental Modal Analysis data
• Vibrational Mode Shapes of a Racquetball Racket (added 12/9/2010) - Bending, Torsional and Membrane modes in a racket.
• Vibrational Modes of an Acoustic Guitar - actual experimental Modal Analysis data
• Tacoma Narrows Bridge - (0.668 MB mpeg movie) - when engineers don't account for resonance when designing structures
• Motion of the Center-of-Mass - not exactly acoustics and vibration, but the animations are cool

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