ISSN:0002-9505    

DOI:10.1119/1.17229

出版商:American Association of Physics Teachers    

年代:1993

数据来源: AIP

摘要:

An impulsive point excitation in a linear, nondispersive wave medium can produce an after‐signal, which has been called a ‘‘wake’’ in the mathematical physics literature. Relations are derived between such wakes and the dimensionality of the space by regarding a point source in space of dimensionalityN−2 as a line source inN−1 dimensions and as a plane source inNdimensions. The ‘‘magic’’ of one and three dimensions is discussed from a new point of view.

ISSN:0002-9505    

DOI:10.1119/1.17230

出版商:American Association of Physics Teachers    

年代:1993

数据来源: AIP

摘要:

The exponential divergence of chaotic trajectories of a driven nonlinear oscillator is considered. A particularly simple method of determination of the Lyapunov exponents of experimental data is shown to yield quantitative estimates which scale with the control parameter of the system in accord with expectation. Numerical comparisons with conventional approaches, which are unsuited to pedagogic use, demonstrate the adequacy of the present method in this context.

ISSN:0002-9505    

DOI:10.1119/1.17231

出版商:American Association of Physics Teachers    

年代:1993

数据来源: AIP

摘要:

A classroom demonstration based on computer animation illustrates chaotic motion in a driven pendulum. Generated by a 76 line BASIC program that runs on PC‐compatible computers, the animation shows four simultaneous displays, including the pendulum and its trajectory in state space. The program can be used to illustrate periodic attractors, symmetry breaking, period doubling, and chaos.

ISSN:0002-9505    

DOI:10.1119/1.17232

出版商:American Association of Physics Teachers    

年代:1993

数据来源: AIP

摘要:

The violin supports a Helmholtz resonance, acting like a driven, damped harmonic oscillator. The amount of damping can be measured from the width of the response curve, and also from the decay of an undriven oscillator. The phase shift between driver and resonator is also consistent with theory. Shifts in resonant frequency due to changing the aspect ratio of the f hole are measured and found to be in qualitative agreement with a convenient formula for the resonant frequency associated with a long thin aperture.

ISSN:0002-9505    

DOI:10.1119/1.17233

出版商:American Association of Physics Teachers    

年代:1993

数据来源: AIP

摘要:

A simple and pedagogical kinematic experiment to measure the mass‐size fractal dimensionDof crumpled surfaces is presented. The experiment is inspired in the well‐known Galilean experiments with bodies rolling on inclined planes. The experimental results forDagree with those obtained from static means.    

ISSN:0002-9505    

DOI:10.1119/1.17234

出版商:American Association of Physics Teachers    

年代:1993

数据来源: AIP

摘要:

The specific example of an electron orbiting in the field of a charged sphere and a superimposed uniform magnetic field is used to illustrate that in classically chaotic systems, irreducible uncertainties required by the Heisenberg principle are amplified exponentially to the macroscopic level in short times. According to the Copenhagen interpretation of quantum theory irreducible quantum uncertainties have led to quantum indeterminacy on a macroscopic scale in interesting times.

ISSN:0002-9505    

DOI:10.1119/1.17235

出版商:American Association of Physics Teachers    

年代:1993

数据来源: AIP

摘要:

It is shown that a previous explanation of the null results of the Trouton‐Noble experiment, as suggested in the literature in terms of a modified definition of energy‐momentum density of electromagnetic fields, is beset with many difficulties. Contrary to what was claimed earlier, a ‘satisfactory’ explanation of the null results of the Trouton‐Noble experiment in no way demands a change in the standard definition of the electromagnetic energy‐momentum density. The pertinent ‘paradox’ of an electromagnetic torque on a freely suspended, charged parallel plate capacitor, as seen from a relatively moving frame of reference, is resolved using the conventional formulation of the energy and momentum densities of electromagnetic fields.

ISSN:0002-9505    

DOI:10.1119/1.17236

出版商:American Association of Physics Teachers    

年代:1993

数据来源: AIP

摘要:

It is sometimes overlooked that a function does not necessarily maximize where its derivative is zero. Oftentimes, a function will maximize at an end point of the range for which it is defined. Thus careful consideration must be given to the range over which functions are valid. In this paper a novel example of such a function is presented and a brief history and review of spherical particle packing in the context of crystallography are given.

ISSN:0002-9505    

DOI:10.1119/1.17237

出版商:American Association of Physics Teachers    

年代:1993

数据来源: AIP

摘要:

Expansion of concentrated functions in terms of a delta function series is discussed with examples. The delta function is extended into the complex plane in the limit of the analytic Gaussian function. It is demonstrated that problems normally handled with the steepest descent method can be simply expressed as an integration of the delta function in the complex plane, which can be more easily grasped by students.

ISSN:0002-9505    

DOI:10.1119/1.17238

出版商:American Association of Physics Teachers    

年代:1993

数据来源: AIP