Related Experiment Video
Updated: Jun 27, 2026

Line Shape Analysis of Dynamic NMR Spectra for Characterizing Coordination Sphere Rearrangements at a Chiral Rhenium Polyhydride Complex
Published on: July 27, 2022
A resonance shift prediction based on the Boltzmann-Ehrenfest principle for cylindrical cavities with a rigid sphere
Arturo O Santillan1, Vicente Cutanda-Henríquez
1Centro de Ciencias Aplicadas y Desarrollo Tecnologico, Universidad Nacional Autonoma de Mexico, Circuito Exterior s/n, Cd. Universitaria, A. P. 70-186, 02510 Mexico, Distrito Federal, Mexico. arturo.orozco@ccadet.unam.mx
Abstract:
An investigation on the resonance frequency shift for a plane-wave mode in a cylindrical cavity produced by a rigid sphere is reported in this paper. This change of the resonance frequency has been previously considered as a cause of oscillational instabilities in single-mode acoustic levitation devices. It is shown that the use of the Boltzmann-Ehrenfest principle of adiabatic invariance allows the derivation of an expression for the resonance frequency shift in a simpler and more direct way than a method based on a Green's function reported in literature. The position of the sphere can be any point along the axis of the cavity. Obtained predictions of the resonance frequency shift with the deduced equation agree quite well with numerical simulations based on the boundary element method. The results are also confirmed by experiments. The equation derived from the Boltzmann-Ehrenfest principle appears to be more general, and for large spheres, it gives a better approximation than the equation previously reported.
Related Concept Videos
Sound Waves: Resonance
Resonance and Hybrid Structures
Resonance Structures and Resonance Hybrids
The Lewis structure of a nitrite anion (NO2−) may actually be drawn in two different ways, distinguished by the locations of the N–O and N=O bonds.
Standing Waves in a Cavity
Spherical and Cylindrical Capacitor
Conventionally, considering the symmetry, the electric field between the concentric shells of a spherical capacitor is directed radially outward. The magnitude of the field, calculated by...
NMR Spectrometers: Resolution and Error Correction
π Electron Effects on Chemical Shift: Aromatic and Antiaromatic Compounds
