VIBRATIONAL MODES.

Film Loop: Vibrations of a Metal Plate

Length: 3:45 Min., Black and White, No Sound

In many finite physical systems, we can generate a phenomenon known as standing waves. A wave in a medium is usually reflected at the boundaries. Characteristic patterns will sometimes be formed, depending on the shape of the medium, the frequency of the wave, and the material. At certain points or lines in these patterns there are no vibrations, because all the partial waves passing through these points just manage to cancel each other out through superposition.

Standing wave patterns only occur for certain frequencies. The physical process selects a spectrum of frequencies from all the possible ones. Often there are an infinite number of such discrete frequencies. Sometimes there are simple mathematical relationships between the selected frequencies, but for other bodies the relationships are more complex. Several films in this series show vibrating systems with such patterns.

The physical system in this film is a square metal plate. The various vibrational modes are produced by a loudspeaker, as with the vibrating membrane in "Vibrations of a Drum". The metal plate is clamped at the center, so that point is always a node for each of the standing wave patterns. Because this is a metal plate, the vibrations are too slight in amplitude to be directly seen. The trick used to make the patterns visible is to sprinkle sand on the plate. This sand is jiggled away from the parts of the plates in rapid motion and tends to fall along the nodal lines. The beautiful patterns of sand are known as Chaladni figures which have often been admired by artists. Similar patterns are formed when a metal plate is excited by means of a violin bow, as seen at the end of the film.

Not all frequencies lead to stable patterns. As in the case of the drum, the harmonic frequencies for the metal plate obey complex mathematical relationships, rather than the simple arithmetic progression seen in a one-dimensional string. But as we scan the frequency spectrum, only certain sharp, well-defined frequencies produce these elegant patterns.