Abstract:
The design, construction, and acoustical measurements of resonators with nonuniform cross-sectional areas that are easily altered to yield different resonance frequencies are described. These resonators are useful as educational demonstrations of symmetry breaking and of an effect of nonuniformity upon standing waves, and have been previously demonstrated and explained [B. Denardo, J. Acoust. Soc. Am. 95, 2935(A) (1994), and B. Denardo and S. Alkov, Am. J. Phys. 62, 315--321 (1994)]. Resonators that yield two, three, and four pitches are considered, where the relative frequencies are designed to correspond to musical intervals. Agreement is within 2% in all cases and 1% for most. The data reveal a breakdown of the theory, which is shown to be a result of additional kinetic energy, and thus effective inertia, near a discontinuity in cross-sectional area. The data also reveal that an appropriate end correction for this case is not that for a thin-walled tube but, rather, an infinite flange.