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Apr 2013

Volume 81, Issue 4, pp. 245-319

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Towards the Kelvin wake and beyond

Andrej Likar and Nada Razpet

American Journal of Physics -- April 2013 -- Volume 81, Issue 4, pp. 245

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The difference between wave propagation in dispersive and non-dispersive media can be effectively demonstrated by observing the wave patterns invoked by uniformly moving surface disturbances. Although the dispersion relation of surface waves on water is complicated, there are some frequency intervals where the phase velocity of the waves reduces to the simple power law behavior cp∝ωκ. Among these cases are gravity waves short compared to the depth of the water (κ = −1), short capillary waves (κ = 1/3), and long waves in shallow water (κ ≈ 0). Making use of this power-law behavior, we vary the exponent and visualize the smooth transition from a non-dispersive to a dispersive medium.
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47.00.00 Fluid dynamics

Elucidating the stop bands of structurally colored systems through recursion

Ariel Amir and Peter Vukusic

American Journal of Physics -- April 2013 -- Volume 81, Issue 4, pp. 253

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Interference is the source of some of the spectacular colors of animals and plants in nature. In some of these systems, the physical structure consists of an ordered array of layers with alternating high and low refractive indices. This periodicity leads to an optical band structure that is analogous to the electronic band structure encountered in semiconductor physics: specific bands of wavelengths (the stop bands) are perfectly reflected. Here, we present a minimal model for optical band structure in a periodic multilayer structure and solve it using recursion relations. The stop bands emerge in the limit of an infinite number of layers by finding the fixed point of the recursion. We compare to experimental data for various beetles, whose optical structure resembles the proposed model. Thus, using only the phenomenon of interference and the idea of recursion, we are able to elucidate the concept of band structure in the context of the experimentally observed high reflectance and iridescent appearance of structurally colored beetles.
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The pilot-wave perspective on quantum scattering and tunneling

Travis Norsen

American Journal of Physics -- April 2013 -- Volume 81, Issue 4, pp. 258

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The de Broglie-Bohm “pilot-wave” theory replaces the paradoxical wave-particle duality of ordinary quantum theory with a more mundane and literal kind of duality: each individual photon or electron comprises a quantum wave (evolving in accordance with the usual quantum mechanical wave equation) and a particle that, under the influence of the wave, traces out a definite trajectory. The definite particle trajectory allows the theory to account for the results of experiments without the usual recourse to additional dynamical axioms about measurements. Instead, one need simply assume that particle detectors click when particles arrive at them. This alternative understanding of quantum phenomena is illustrated here for two elementary textbook examples of one-dimensional scattering and tunneling. We introduce a novel approach to reconcile standard textbook calculations (made using unphysical plane-wave states) with the need to treat such phenomena in terms of normalizable wave packets. This approach allows for a simple but illuminating analysis of the pilot-wave theory's particle trajectories and an explicit demonstration of the equivalence of the pilot-wave theory predictions with those of ordinary quantum theory.
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03.65.-w Quantum mechanics

Coupled second-quantized oscillators

M. Bhattacharya, H. Shi, and S. Preble

American Journal of Physics -- April 2013 -- Volume 81, Issue 4, pp. 267

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Second quantization is a powerful technique for describing quantum mechanical processes in which the number of excitations of a single particle is not conserved. A textbook example of second quantization is the presentation of the simple harmonic oscillator in terms of creation and annihilation operators, which, respectively, represent addition or removal of quanta of energy from the oscillator. Our aim in this article is to bolster this textbook example. Accordingly, we explore the physics of coupled second-quantized oscillators. These explorations are phrased as exactly solvable eigenvalue problems, the mathematical structure providing a framework for the physical understanding. The examples we present can be used to enhance the discussion of second-quantized harmonic oscillators in the classroom, to make a connection to the classical physics of coupled oscillators, and to acquaint students with systems employed at the frontiers of contemporary physics research.
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03.65.-w Quantum mechanics
42.50.-p Quantum optics

A classroom demonstration of reciprocal space

Morten Hannibal Madsen, Louise Høpfner, Nina Rasmussen, Mikkel Stolborg, Jesper Nygård, Robert Feidenhans'l, and Jan W. Thomsen

American Journal of Physics -- April 2013 -- Volume 81, Issue 4, pp. 274

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An array of nanowires and a laser pointer are used for a simple visualization of two-dimensional reciprocal space. The experiment can be performed without any preparation and in any classroom. It aids the teaching of scattering experiments, and illustrates the underlying principles of electron, x-ray, and neutron scattering. A detailed study of the diffraction pattern was performed by mounting the sample with nanowires on a stage designed for x-ray scattering. The setup is well suited for undergraduate students, who get training in sample alignment in a small lab instead of at a large-scale facility. The exact positions of the diffraction spots are calculated and monitored experimentally for a 360° rotation of the sample. By fitting to this set of images, it is possible to determine the lattice vectors of the artificial crystal with an uncertainty of less than 1%.
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01.50.My Demonstration experiments and apparatus
42.00.00 Optics

The rise and fall of spinning tops

Rod Cross

American Journal of Physics -- April 2013 -- Volume 81, Issue 4, pp. 280

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The motion of four different spinning tops was filmed with a high-speed video camera. Unlike pointed tops, tops with a rounded peg precess initially about a vertical axis that lies well outside the top, and then spiral inward until the precession axis passes through a point close to the center-of-mass. The center-of-mass of a top with a rounded peg can rise as a result of rolling rather than sliding friction, contrary to the explanation normally given for the rise of spinning tops. A tippe top was also filmed and was observed to jump vertically off a horizontal surface several times while the center-of-mass was rising, contrary to the usual assumption that the normal reaction force on a tippe top remains approximately equal to its weight. It was found that the center-of-mass of a tippe top rises as a result of rolling friction at low spin frequencies and as a result of sliding friction at high spin frequencies. It was also found that, at low spin frequencies, a tippe top can precess at two different frequencies simultaneously.
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45.00.00 Classical mechanics of discrete systems

Synchronization of a thermoacoustic oscillator by an external sound source

G. Penelet and T. Biwa

American Journal of Physics -- April 2013 -- Volume 81, Issue 4, pp. 290

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Since the pioneering work of Christiaan Huygens on the sympathy of pendulum clocks, synchronization phenomena have been widely observed in nature and science. In this paper, we describe a simple experiment, with a thermoacoustic oscillator driven by a loudspeaker, which exhibits several aspects of synchronization. Both the synchronization region of leading order around the oscillator's natural frequency f0 and regions of higher order (around f0∕2 and f0∕3) are measured as functions of the loudspeaker voltage and frequency. We also show that increasing the coupling between the loudspeaker and the oscillator gives rise under some circumstances to the death of self-sustained oscillations (quenching). Moreover, two additional set of experiments are performed: the first investigates a feedback loop in which the signal captured by the microphone is delivered to the loudspeaker through a phase-shifter; the second investigates the nontrivial interaction between the loudspeaker and the oscillator when the latter acts as a relaxation oscillator (spontaneous and periodic onset/damping of self-sustained oscillations). The experiment is easy to build and highly demonstrative; it might be of interest for classroom demonstrations or an instructional lab dealing with nonlinear dynamics.
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05.45.-a Nonlinear dynamics and chaos
43.00.00 Acoustics

A missing magnetic energy paradox

Constantino Grosse

American Journal of Physics -- April 2013 -- Volume 81, Issue 4, pp. 298

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While the interaction forces between two electric and two magnetic dipoles are formally identical, their interaction energies differ because in addition to mechanical work, the magnetic energy includes the electrical work needed to keep the dipole moments unaltered. This energy difference appears to contradict a calculation based on the integrals of the squares of the electric and magnetic fields since the electric and magnetic dipole fields have precisely the same geometry.
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41.00.00 Electromagnetism; electron and ion optics
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University student and K-12 teacher reasoning about the basic tenets of kinetic-molecular theory, Part I: Volume of an ideal gas

Amy D. Robertson and Peter S. Shaffer

American Journal of Physics -- April 2013 -- Volume 81, Issue 4, pp. 303

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This article reports on a long-term investigation of student and teacher reasoning about the basic tenets of kinetic-molecular theory as they relate to the concept of volume. This research grew out of the finding that university-level students and practicing K-12 teachers often treat the volume of a gas as different from that of its enclosing container. We examined the extent to which this tendency might be associated with incorrect reasoning about the motions of the particles in the gas. The results suggest that teachers and students often justify incorrect answers about the volume of a gas with incorrect statements about the motion of gas particles.
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01.40.Fk Research in physics education
05.00.00 Statistical physics, thermodynamics, and nonlinear dynamical systems
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Unintended consequences of imprecise notation: An example from mechanics

Asim Gangopadhyaya and Gordon Ramsey

American Journal of Physics -- April 2013 -- Volume 81, Issue 4, pp. 313

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We present a conundrum that results from the imprecise use of notation for partial derivatives. Taking an example from mechanics, we show that lack of proper care in representing partial derivatives in the Lagrangian and Hamiltonian formulations paradoxically leads to two different values for the time derivative of the canonical momentum. Similar apparent paradoxes occur in other areas of physics, such as thermodynamics.
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45.00.00 Classical mechanics of discrete systems
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HIGGS: The Invention and Discovery of the “God Particle.”

Jim Baggott and Mano Singham, Reviewer

American Journal of Physics -- April 2013 -- Volume 81, Issue 4, pp. 316

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Abstract Unavailable
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01.30.Vv Book reviews
01.65.+g History of science

A General Relativity Workbook.

Thomas A. Moore and Thomas W. Baumgarte, Reviewer

American Journal of Physics -- April 2013 -- Volume 81, Issue 4, pp. 317

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Abstract Unavailable
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01.30.Vv Book reviews
04.00.00 General relativity and gravitation

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American Journal of Physics -- April 2013 -- Volume 81, Issue 4, pp. 319

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