## Album of animations, demonstrating oscillations, waves, and phasors

#### with links to the animations and explanatory text. Illustrations are for adding interest to the physics. These can be turned on and off by clicking on the +/− symbol on the animations. Once you have downloaded an animation, mouse over it to see the action. P. Ceperley, Jan07

Plotting the sine function

Animation of the creation of a sine function from the definition of sine as a ratio of sides of a right triangle.

AC voltage

Flash clip showing a voltmeter swinging madly back and forth because of AC power.

Animation of the basic phasor rotor

A rotating vector and its projection make up the central idea behind the phasor representation of oscillations and waves. This animation illustrates this principle.

Animation showing phasor, graph, and bungy jumper

Animation showing the relationship between a phasor, a graph, and an oscillation. The oscillations is that of a person bobbing up an down on the end of a bungy cord.

Addition of phasors with bungy jumpers

Animation showing the relationship between two phasors, their sum, their graphs, and the oscillations they represent. The oscillations are of two people bobbing up and down on the end of bungy cords.

Beating of two oscillations

Animation showing the beating of two oscillations. The oscillations are those of two people on the ends of their respective bungy cords. Phasors and graphs are created as the animation proceeds.

Beating tones

Flash file allowing the viewer to listen to several audio files demonstrating the beating of tones.

Complex rotor, ball goddess

Decorative animation of the complex rotor.

Complex exponential function, a show stopper

Animation of the complex rotor, the central idea behind phasors based on complex number.

Complex phasors, da Vinci

Animation showing the relationship between an oscillating variable, a voltage in this case, and a complex phasor. This animation also shows a graph of the oscillating quantity.

Complex multiplication of a phasor, beaches

Animation showing the relationship between a phasor and a second product phasor that results from multiplying the first phasor by a complex constant. This also shows the oscillating quantities, temperatures in this case, and a graph of the two oscillations.

Gaussian solitary wave, skateboard

Animation showing the time dependence of a solitary wave, i.e. a gaussian function, written as a function of xct.

Shifted gaussian, leprechaun

Animation showing the shifting of a stationary gaussian function due to changing the x offset.

Traveling Wave, carhop

Animation showing the time dependence of a continuously shifting cosine function, that is in fact a traveling wave.

General equation for a traveling wave

Animation showing the dependence the various parameters in the general equation for a traveling wave . The user can change the values of these parameters and see the effect on the animated traveling wave.

Complex phasors of a traveling wave

Animation showing the relationship between a traveling wave and the complex phasors at various points along the wave.

Traveling wave as a complex helical wave

Animation showing the relationship between a traveling wave and the complex phasors at various points along the wave. In this animation we show the wave in its complex form, as a helical wave with one axis along the imaginary direction.

Traveling wave by a monkey

Animation showing a one dimensional traveling wave on a rope.

Traveling 2D wave on a mesh

Animation showing a two dimensional traveling wave on a mesh. The wave is aligned with one axis of the mesh.

Oblique traveling mesh wave

Animation showing a two dimensional traveling wave on a mesh. The wave is propagating at a 30 degree angle to the mesh axes.

Circular traveling wave

Animation showing a spreading circular wave on a mesh.

Electromagnetic traveling wave

Animation showing the propagation of an electromagnetic wave. The time varying electric and magnetic field vectors are shown. The viewer can adjust the viewing angle.

Animation of a sound wave

Animation showing a slow longitudinal pressure wave (i.e. a very slow sound wave) propagating in an array of compressible balls. This is one form of traveling waves. The viewer can choose to see the phasors for the waves in each ball. He or she can also choose to introduce attenuation in the wave.

Spark gap transmitter

Animation showing the operation of a sparkgap transmitter, used by Marconi and others in the early days of radio.