Demos about Waves

(Note: For many of these animations, the QuickTime 7 plugin for Firefox will only show the first second of time.  Download the file instead.)

Oscillations:

There is a close relationship between waves and oscillations.  This Excel spreadsheet allows you to vary the parameters in a cosine oscillation, to see how it effects the graph. (Requires Excel)

Oscillations are also closely related to rotating circles, as illustrated here and also here.  (The second one comes from the Geometer's Sketchpad Resource Center.)

Superposition:

This Excel spreadsheet makes it easy to superpose two cosine oscillations. (Requires Excel)

"Adding Waves": (under "Experiments on Wave Interference", scroll down to first Applet):  Really excellent addition of two waves.  Move the red and gray balls, or move the entire waves in the upper panels.  See if you can make convincing beats (hint: use a short wavelength).  (from Physics 2000, which has a variety of excellent applets)

This Excel spreadsheet is very similar to the previous one, but it adds 6 cosine oscillations together.  Note that in this you specify frequency, while in the previous one you specify period. (Requires Excel)

A Fourier Synthesizer (from Virtual Physics Laboratory)

Types of Waves:

There are many different kinds of waves, with different characteristics.  (page by Dan Russell of Kettering University)

This interactive wave applet lets you make transverse waves directly. (from among the many neat Java applets are available from the University of Colodaro)

Longitudinal waves can be described by their displacement or their density. This PDF shows how those relate.

Waves in Space and Time:

Waves have different values at different places and different times.

• Values at different places can easily be shown with a position graph, essentially a snapshot of the wave.
• Values at different times can be harder to imagine.
  • In these animations (AVI) watch the BLUE CIRCLE to view the motion of a single point for either an irregular wave of a sinusoidal wave.  (In the second case, the point executes Simple Harmonic Motion.)
  • You can graph the position of one point of the medium versus time, showing how it oscillates.  (see "Oscillations" above.)

Sound:

Sounds have pitches depending on the sound wave's frequency.  Click here to hear a function generator sweep the entire audible range of frequencies (20 Hz to 20 kHz).  It's supposed to be pure tones, although distortion in the speaker used lead to some higher harmonics, especially for the lower pitches.

Speed of sound in various materials, and here too (and here is a site with an extensive list for woods)

Here is a graph of the frequencies of the notes in the equal temperament musical scale.  Note that on a linear graph axis, the notes get more widely spaced at higher frequencies.  The musical notes are spaced at equal ratios of frequency, not equal increments of frequency.

Huygen's Wavelets:

The following "animations" illustrate that a set of closely spaced point sources nicely approximates a non-point source.  The motion in the movies does not represent anything evolving in time.  Instead, each frame represents a snapshot of a wave with a particular source configuration.

• This primarily illustrates that a line of point sources looks like a linear source, if the source is large enough compared to the wavelength.
• This has the same setup, but focusses on the end of the line of sources.  As justified by Huygen's wavelets, this is equivalent to a wave passing through a hole.  You can see that the smaller hole, the more the wave diffracts around the corner.
• This focusses on the end of a long line of sources.  As justified by Huygen's wavelets, the is equivalent to a wave passing by an edge.  Here the wavelength is varied, and you can see that longer wavelengths diffract slightly more.