Thursday, June 12, 2008

Sound Waves

Thanks to Homeschooled Twins for pointing to this awesome demonstration of the vibrations of sound waves.


Kim said...

To me they look like interference fringe patterns. The sound wavelength has to be a factor of the distance between the patterns.

Kim said...

But I can see I have a new homeschooling blog to read! Thanks for pointing it out!

Joe said...

LB: great video!

Kim: Not quite fringe patterns. Here’s the short (!) version:

The square plate you see is being shaken (“excited”) by a motor vibrating at increasing frequencies. When the shaker reaches a specific “natural frequency” of the plate, the plate vibrates strongly (i.e. it resonates). The vibration consists of back-and-forth motion in a specific pattern, or “mode shape”. In each of these modes, some parts (or zones) of the plate are moving up and down, while other neighboring parts/zones are simultaneously moving in the reverse direction (i.e. down and up). The white lines highlight the mode shape, or more specifically the boundaries between the zones; the powder collects here since these boundaries don’t move up and down – i.e. you get something like a trough where the powder collects when it is bounced off the moving zones.

When the shaker vibrates at a frequency between the object’s natural frequencies, the vibration amplitude is minimal, and the distinct mode shapes are not apparent.

A simpler example of this phenomenon is a one-dimensional counterpart to the two dimensional plate above: A vibrating string under tension sways back and forth under excitation at its lowest natural frequency. At the next higher natural frequency, the vibration pattern is a reversing S-shape, i.e. there is one point (in the middle of the S) that is motionless, called a node, while on either side the string moves back and forth. At the next frequency the pattern is a reversing W (two nodes), and so on. Here, the nodal points are the one-dimensional counterpart to the white nodal lines in the two-dimensional plate example above. If you observed the edge of a slice through the plate while it was vibrating, you would see similar S shapes.

LB said...

Thanks, Joe, for the great explanation. We were wondering what part the shape of the plate played, if any, in the patterning.

Kim, happy to share!

Joe said...

... and here are some animations for various objects:

(See the links in the section "Vibrational Modes of Continuous Systems")