ANOMALOUS DISPERSION OF SOUND IN SOLID CYLINDRICAL RODS

1935 ◽  
Vol 13a (1) ◽  
pp. 10-15 ◽  
Author(s):  
R. Ruedy
Keyword(s):  
Mutual Coupling ◽  
Radial Component ◽  
Radial Motion ◽  
Coupled Systems ◽  
Radial Vibration ◽  
Longitudinal Waves ◽  
Velocity Equation ◽  
Hollow Cylinders ◽  
Velocity Of Propagation ◽  
Set Up

The deviation of the overtones from whole multiples of the fundamental note when pure longitudinal waves are set up in a cylindrical rod, one to a few centimetres in thickness, is accounted for to within less than 1% by the drop in the velocity of propagation of longitudinal waves with increasing frequency due to radial motion in the rod. The radial component present in vibrating solid or hollow cylinders determines a second solution of the velocity equation which starts near the resonance frequency of the radial vibration. Although radial motion can take place free from longitudinal components, so that no mutual coupling need exist between the two types of vibration, the equation for thin rods can within certain frequency ranges be reduced to the frequency relations valid for coupled systems.

ON THE PROPAGATION OF LONGITUDINAL WAVES IN CYLINDRICAL RODS

1931 ◽  
Vol 5 (2) ◽  
pp. 149-155 ◽  
Author(s):  
R. Ruedy
Keyword(s):  
Coupled System ◽  
Theory Of Elasticity ◽  
Radial Vibrations ◽  
Low Frequencies ◽  
Longitudinal Waves ◽  
Resonance Frequencies ◽  
Solid Circular Cylinder ◽  
Velocity Equation ◽  
Set Up ◽  
Degree Of Coupling

The solution of the velocity equation obtained by Pochhammer on the basis of the mathematical theory of elasticity is determined for the propagation of longitudinal waves of any frequency in a long solid circular cylinder of any diameter. For a given frequency a large number of solutions may be obtained, but when the condition is imposed that for low frequencies the velocity must gradually assume the value found by experiment, a single value is obtained for each frequency. The velocity decreases with increasing frequency, so that, for a cylinder of finite length, the resonance frequencies come closer and closer together. It is also necessary to take into account, however, that in a solid rod longitudinal waves are accompanied by radial vibrations of the particles, and that a cylindrical rod has, regardless of its length, a series of natural frequencies for radial waves, so that for wave-lengths comparable with the diameter of the tube a coupled system of oscillations is set up. The resonant frequencies of such a system depend on the degree of coupling.

High Density Bulk Shape Rapid Consolidation of the Yba2Cu307-X Superconductor

1989 ◽  
Vol 169 ◽  
Author(s):  
S. V. Rele ◽  
R. V. Raman ◽  
H. S. Meeks ◽  
R. L. Anderson ◽  
R. N. Shelton ◽  
...  
Keyword(s):  
Volume Fraction ◽  
X Ray Diffraction ◽  
X Ray ◽  
Superconducting Volume Fraction ◽  
One Step ◽  
Hollow Cylinders ◽  
Diffraction Patterns ◽  
Set Up ◽  
Cylinders And Spheres ◽  
High Processing

AbstractA novel rapid densification technique for fabrication of bulk shape YBa2Cu307–xsuperconductor is presented. The Ceracon process is a one‐step, quasi‐isostatic consolidation route utilizing conventional P/M equipment and set‐up. The Ceracon technology has enabled successful fabrication of bulk, shapes such as discs, cylinders, hollow cylinders and spheres along with significant increases in the density up to 95‐98% of the theorertical. The superconducting volume fraction is preserved due to short hold times at the operating temperatures and avoidance of high processing temperatures. Results based on densities, microstructure, susceptibility measurements, X‐ray diffraction patterns and TGA measurements are discussed.

scholarly journals Further investigation of the velocity of propagation of light in vacuo in a transverse magnetic field

1940 ◽  
Vol 175 (960) ◽  
pp. 1-25 ◽  
Keyword(s):  
Magnetic Field ◽  
Transverse Magnetic Field ◽  
Transverse Magnetic ◽  
The Other ◽  
Velocity Of Light ◽  
Propagation Of Light ◽  
Leakage Field ◽  
Velocity Of Propagation ◽  
Set Up ◽  
The Magnetic Field

In a previous paper (1932) an attempt to measure the effect, if any, of a transverse magnetic field on the velocity of light in vacuo was described. No change greater than 1 part in 2 x 10 7 was found in a field of 18,000 oersted. As the Jamin interferometer used had certain drawbacks for an experiment of this kind, it was decided to set up a Michelson type of interferometer, the use of which might be expected to avoid some of these difficulties and increase the sensitivity. In particular, one of the interfering rays could be made to pass twice through the magnetic field, or, by means of auxiliary mirrors, a multiple of this, while the other interfering ray, being at right angles to the first, was well away from the vicinity of the main leakage field, which would have a compensating effect as far as any change in velocity was concerned.

A Lorentz Invariant Schrödinger Equation for Spin 0

1989 ◽  
Vol 44 (9) ◽  
pp. 801-810
Author(s):  
E. Trübenbacher
Keyword(s):  
Particle Trajectory ◽  
Relativistic Quantum ◽  
Wave Functions ◽  
Relativistic Quantum Mechanics ◽  
Practical Application ◽  
Vector Potentials ◽  
Component Wave ◽  
Velocity Of Propagation ◽  
Set Up ◽  
A Current

Abstract Using the concept of distributions, the square root of the operator - Δ + m2 is taken in a mathematically well defined way for one component wave functions. A new representation of proper Lorentz transformations for one component wave functions makes it possible to construct a relativistic quantum mechanics for spin 0, comprising a Lorentz invariant wave equation, a scalar product, and a positive definite density satisfying, together with a current, a continuity equation, and coupling of scalar and vector potentials. Some interesting consequences of the theory concerning the concept of particle trajectory and velocity of propagation of the probability amplitude are discussed in detail. As an example of practical application a perturbation theory for discrete states is set up.

scholarly journals On the Reconstruction Capability of the Linear Sampling Method

2018 ◽  
Vol 5 (1) ◽  
Author(s):  
Morteza Ghaderi Aram
Keyword(s):  
Qualitative Method ◽  
Mutual Coupling ◽  
Sampling Method ◽  
Reconstruction Algorithm ◽  
Measured Data ◽  
Reference Scenario ◽  
Linear Sampling Method ◽  
Set Up ◽  
Measurement Chamber ◽  
Linear Sampling

<p>Linear Sampling Method (LSM), although a simple and fast qualitative method, encounters some limitations and restrictions when it comes to measurement set-up and realistic implementation. Addressing some difficulties arising from somewhat complicated measurement structures used to gather raw data for the reconstruction algorithm, this communication tries to show the effect of mutual coupling between antennas utilized in the measurement chamber. Another tangible effect of the antenna arrangement, covered here through reconstructing a reference scenario of Fresnel Institute dataset, has to do with the aspect-limited nature of scan lines. Reconstructions based on both simulated and measured data are reported.</p>

An analytical model of cymbal transducer dynamics. Radial vibration of a piezoelectric disc

2011 ◽  
Vol 225 (5) ◽  
pp. 1077-1086 ◽  
Author(s):  
O A Ganilova ◽  
M Lucas ◽  
A Cardoni
Keyword(s):  
Analytical Model ◽  
Compressive Loading ◽  
Electrical Potential ◽  
Electrical Signal ◽  
Radial Motion ◽  
Coupled Systems ◽  
Cymbal Transducer ◽  
End Caps ◽  
Piezoelectric Disc ◽  
Radial Behaviour

This article represents the first step in an attempt to obtain an analytical model of a cymbal transducer. The structure is considered as two mechanically coupled systems (i.e. a piezoelectric disc producing radial motion and end caps amplifying under the compression caused by this radial behaviour). Therefore, an analytical model of the piezoelectric disc, core driver of the cymbal, and its dynamics under an electrical signal are presented in this article. The function describing the radial motion of the disc, distribution of the electrical potential along the thickness, and displacement along the thickness are obtained analytically. The obtained radial motion function will be used for modelling the end cap amplification as a compressive loading.

Hydrogen-like Atomic Wavefunctions: A First Sketch

2020 ◽  
pp. 99-108
Author(s):  
Jochen Autschbach
Keyword(s):  
General Chemistry ◽  
Fixed Point ◽  
Angular Momentum ◽  
Point Charge ◽  
Radial Component ◽  
Polar Coordinates ◽  
Angular Momentum Quantum Number ◽  
Quantum Numbers ◽  
Set Up ◽  
Atomic Wavefunctions

This chapter reiterates the quantum numbers for atomic orbitals, known from general chemistry, and places them into the context developed so far. It is sketched how the Schrodinger equation (SE) for the hydrogen atom hydrogen-like systems (one electron plus a nucleus of charge Z) is set up. When the nucleus is treated as a fixed point charge, the SE is only for the electron. The solutions of the SE can be obtained by switching to spherical polar coordinates, such that the variables are separable in terms of the electron distance from the nucleus, r, and two angles. The kinetic energy of the electron then has a radial component, and an angular component. The latter is associated with the angular momentum quantum number, which is codified by the letters s, p, d, f, and so forth. A step by step solution of the SE is provided later, in chapter 19.

Calculation of Wave Velocities in Segmented Pipelines with Flexible Joints

2020 ◽  
pp. 3-17
Author(s):  
M. Sh. Israilov ◽  
L. N. Smirnova
Keyword(s):  
Periodicity Cell ◽  
Flexible Joints ◽  
Accurate Analysis ◽  
Longitudinal Waves ◽  
One Dimensional ◽  
Average Value ◽  
Wave Velocities ◽  
Long Wave ◽  
Order Of Magnitude ◽  
Velocity Of Propagation

Engineering methods for finding the average (averaged) velocity of propagation of longitudinal waves in pipelines with flexible joints are presented. By accurate analysis of the problem of oscillations of a one dimensional periodically inhomogeneous structure it is shown that the results of engineering approaches for rod velocity are the first or long-wave asymptotic approximation which valid when the period of external influence (the length of the seismic wave) significantly exceeds the size of the periodicity cell of the pipeline (the length of the pipe with a joint). Thus, it is established that when this condition is met, the problem of pipeline dynamics with joints is reduced to a much simpler problem of vibrations of a homogeneous pipeline, the velocity of wave propagation in which is equal to the found average value. Numerical examples are given that demonstrate a significant (sometimes by an order of magnitude) decreasing of the rod velocity in the presence of flexible joints.

The Effects of Drying Techniques on Clay-Rich Soil Texture

1974 ◽  
Vol 32 ◽  
pp. 466-467
Author(s):  
T. G. Naymik
Keyword(s):  
Critical Point ◽  
Liquid Nitrogen ◽  
Liquid Nitrogen Temperature ◽  
Drying Methods ◽  
Air Drying ◽  
Freeze Dried ◽  
Critical Point Drying ◽  
Set Up ◽  
The Relationship ◽  
Quartz Grains

Three techniques were incorporated for drying clay-rich specimens: air-drying, freeze-drying and critical point drying. In air-drying, the specimens were set out for several days to dry or were placed in an oven (80°F) for several hours. The freeze-dried specimens were frozen by immersion in liquid nitrogen or in isopentane at near liquid nitrogen temperature and then were immediately placed in the freeze-dry vacuum chamber. The critical point specimens were molded in agar immediately after sampling. When the agar had set up the dehydration series, water-alcohol-amyl acetate-CO2 was carried out. The objectives were to compare the fabric plasmas (clays and precipitates), fabricskeletons (quartz grains) and the relationship between them for each drying technique. The three drying methods are not only applicable to the study of treated soils, but can be incorporated into all SEM clay soil studies.

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