Order Resonant Frequencies Research Articles

The vibrating wire viscometer as a magnetic field-independent3He thermometer

An analysis of the semicircular loop, vibrating-wire3He viscometer has been made. Emphasis was placed upon the magnetic field dependence of the resonance frequency and frequency width (damping) in order to study the suitability of the device for a field-independent thermometer. The analysis was complemented by experiments with Ta, Nb-Ti, Cu, Ag, Au, and Cu-Ni wires. It was found that the various wires, whether superconducting or pure or impure normal metals, have advantages and disadvantages. The superconducting wires show a large field-dependent frequency shift due to induced magnetization and a field-dependent damping due to flux motion. Pure normal metals also show induced magnetization (eddy-current) frequency shift and damping, and impure metals and alloys give Joule heating. Nevertheless, it is shown that the device can be used in the range 1–10 mK and for fields from 20 mT to 1 T.

Simple Approximate Expressions for Higher Order Mode Cutoff and Resonant Frequencies in TEM Cells

Simple approximate expressions for determining the cutoff frequencies of the first few higher order modes and the associated resonant frequencies in transverse electromagnetic (TEM) cells are presented. Both symmetric (seven TE and two TM modes) and asymmetric (three TE modes) cells are discussed.

Acoustic scattering by baffled membranes

A flexible membrane is set in an infinite plane baffle. The plane separates an acoustic field from a vacuum. A time harmonic wave is incident from the fluid on the membrane. When the frequency of the incident wave is not close to an in-vacuo resonant frequency of the membrane, the reaction of the fluid on the membrane is small. However, near a resonant frequency the fluid–membrane coupling is significant. We use the method of matched asymptotic expansions to obtain an asymptotic expansion of the scattered field. It is uniformly valid in the incident frequency. The expansion parameter ε≪1 is the ratio of the fluid and membrane densities. The outer expansion, valid away from resonance, is O(ε). The inner expansion, valid near resonance, is of order unity. The fluid loading is shown to have the effect of decreasing the resonant frequencies from those of the in-vacuo membrane. Simple and double resonant frequencies are analyzed. However, the method is applicable to higher order resonant frequencies. Finally, the method is applied to normal incidence of a plane wave on a circular membrane.

Experimental studies on fourth sound in superfluid helium

In a superfluid liquid-helium cavity packed with a fine powder, only the supercomponent is free to move and pressure waves transmitted by the supercomponent are called “fourth sound.” We have observed that the resonance frequency of the powder-filled chamber may be shifted by introducing vortices. Both static and dynamic measurements were made on the resonance frequency and signal height in order to explore the effect of exceeding the critical velocity of the superfluid in the powder-filled chamber.