Film loop: "Vibrations of a drum", 3:25 min.

Film Loop: Vibrations of a Drum Length (min.):3:25 Color: No Sound: No In many finite physical systems, we can generate a phenomenon known as standing waves. A wave in a medium is 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 standing wave patterns in this film are in a stretched, circular, rubber membrane driven by a loudspeaker. The loudspeaker is fed about 30 watts of power. The sound frequency can be changed electronically. The lines drawn on the membrane make it easier to see the patterns. The rim of the drum can not move, so it must be in all cases a nodal circle, a circle which does not move as the waves bounce back and forth on the drum. By operating the camera at a frequency only slightly different from the resonant frequency, we get a stroboscopic effect enabling us to see the rapid vibrations as if they were in slow-motion. In the first part of the film, the loudspeaker is directly under the membrane, and the vibratory patterns are symmetrical. In the fundamental harmonic, the membrane rises and falls as a whole. At a higher frequency a second circular node shows up between the center and the rim. In the second part of the film, the speaker is placed to one side, so that a different set of modes, asymmetrical modes, are generated in the membrane. There will be an anti-symmetrical mode where there is a node along the diameter, with a hill on one side and a valley on the other. Various symmetric and anti-symmetric vibration modes are shown. Describe each mode, identifying the nodal lines and circles. In contrast to the one-dimensional hose in "Vibrations of a Rubber Hose" there is no simple relationship between resonant frequencies for this system. The frequencies are not integral multiples of any basic frequency. The relationship between values in the frequency spectrum is more complex than the values for the hose.