Normal Modes of a Circular Membrane
Safety Warnings
Warning: Volume Control
Purpose
Visualizes normal mode vibrations of a circular membrane using a speaker-driven soap film and optical projection. Students observe distinct nodal patterns at resonant frequencies, extending standing wave concepts from 1D strings to 2D membranes described by Bessel functions.
Figure 1:
Soap film driven at a resonant frequency showing concentric circular nodal rings. Thin-film interference colors make the nodal pattern visible.
Figure 2:
A higher-order normal mode with both circular and radial nodal lines, showing more complex Bessel function structure.
Figure 3:
Complete setup: fiber optic light source and collimating lens on optical rail, plexiglass cylinder for the soap film over a solution tray, speaker in wooden box, and signal generator.