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Mar 2009

Volume 77, Issue 3, pp. 197-288

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A balloon lens: Acoustic scattering from a penetrable sphere

Derek C. Thomas, Kent L. Gee, and R. Steven Turley

American Journal of Physics -- March 2009 -- Volume 77, Issue 3, pp. 197 | Cited 3 times

Online Publication Date: Feb 2009

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A balloon filled with a gas that has a different sound speed than that of air has been used as an acoustic lens. One purpose of the lens is to show refraction of sound waves in an analogy to geometric optics. We discuss the physics of the balloon lens demonstration. To determine the validity of a gas-filled balloon as a classroom demonstration of an acoustic lens and to understand the corresponding phenomena, its physics is considered analytically, numerically, and experimentally. Our results show that although a geometric analogy is a good first-order approximation, scattering theory is required to fully understand the observed phenomena. Thus this demonstration can be adapted to a wide range of students, from those learning the basic principles of refraction to advanced students studying scattering.
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01.50.My Demonstration experiments and apparatus
43.00.00 Acoustics

Laboratory exercises on oscillation modes of pipes

Willy Haeberli

American Journal of Physics -- March 2009 -- Volume 77, Issue 3, pp. 204

Online Publication Date: Feb 2009

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This paper describes an improved lab setup to study the vibrations of air columns in pipes. Features of the setup include transparent pipes which reveal the position of a movable microphone inside the pipe; excitation of pipe modes with a miniature microphone placed to allow access to the microphone stem for open, closed, or conical pipes; and sound insulation to avoid interference between different setups in a student lab. The suggested experiments on the modes of open, closed, and conical pipes, the transient response of a pipe, and the effect of pipe diameter are suitable for introductory physics laboratories, including laboratories for nonscience majors and music students, and for more advanced undergraduate laboratories. For honors students or for advanced laboratory exercises, the quantitative relation between the resonance width and damping time constant is of interest.
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01.50.Pa Laboratory experiments and apparatus
43.00.00 Acoustics

A demonstration of rotating sound waves in free space and the transfer of their angular momentum to matter

Arturo O. Santillán and Karen Volke-Sepúlveda

American Journal of Physics -- March 2009 -- Volume 77, Issue 3, pp. 209 | Cited 1 time

Online Publication Date: Feb 2009

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We describe an apparatus for generating rotating sound waves in free space by superimposing two orthogonal standing modes with a quarter wave phase lag. The creation of a standing wave from the superposition of two counter-rotating waves is also possible with the same apparatus. The experiment permits direct measurement of both the amplitude and phase structure of the sound waves. A demonstration of angular momentum transfer from rotating acoustic waves to matter in free field is also described.
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01.50.Pa Laboratory experiments and apparatus
43.00.00 Acoustics

Dynamics of a double pendulum with distributed mass

M. Z. Rafat, M. S. Wheatland, and T. R. Bedding

American Journal of Physics -- March 2009 -- Volume 77, Issue 3, pp. 216 | Cited 1 time

Online Publication Date: Feb 2009

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We investigate a variation of the simple double pendulum in which the two point masses are replaced by square plates. The double square pendulum exhibits richer behavior than the simple double pendulum and provides a convenient demonstration of nonlinear dynamics and chaos. It is also an example of an asymmetric compound double pendulum, which has not been studied in detail. We obtain the equilibrium configurations and normal modes of oscillation and derive the equations of motion, which are solved numerically to produce Poincaré sections. We show how the behavior varies from regular motion at low energies, to chaos at intermediate energies, and back to regular motion at high energies. We also show that the onset of chaos occurs at a significantly lower energy than for the simple double pendulum.
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05.45.-a Nonlinear dynamics and chaos

How fast could Usain Bolt have run? A dynamical study

H. K. Eriksen, J. R. Kristiansen, Ø. Langangen, and I. K. Wehus

American Journal of Physics -- March 2009 -- Volume 77, Issue 3, pp. 224 | Cited 3 times

Online Publication Date: Feb 2009

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Since that memorable day at the Beijing 2008 Olympics, a big question has been, “What would the 100 m dash world record have been had Usain Bolt not celebrated at the end of his race?” Bolt’s coach suggested that the time could have been 9.52 s or better. We consider this question by measuring Bolt’s position as a function of time using footage of the run, and then extrapolate the last 2 s with two different assumptions. First, we conservatively assume that Bolt could have maintained the runner-up’s acceleration during the end of the race. Second, based on the race development prior to the celebration, we assume that Bolt could have kept an acceleration of 0.5 m∕s2 greater than the runner-up. We find that the new world record in these two cases would have been 9.61±0.04 and 9.55±0.04 s, respectively, where the uncertainties denote 95% statistical errors.
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01.55.+b General physics

Generation of Bessel beams using a 4-f spatial filtering system

Jeremy M. D. Kowalczyk, Stefanie N. Smith, and Eric B. Szarmes

American Journal of Physics -- March 2009 -- Volume 77, Issue 3, pp. 229 | Cited 2 times

Online Publication Date: Feb 2009

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We demonstrate a simple and straightforward method of producing Bessel beams using a 4-f spatial filtering system that requires no specialized optical components. The experiment employs the established technique of diffraction from a thin ring source, but the ring source is produced by the high-pass filtering of a uniformly illuminated circular aperture, yielding Bessel beams with a central spot radius of less than 35 μm which persist over a distance of 160 mm. The experiment unifies diffraction theory, Fourier optics, and the properties of Bessel beams in a manner appropriate for an advanced undergraduate laboratory.
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01.50.Pa Laboratory experiments and apparatus
42.00.00 Optics

Scattering of a nonuniform wave by a thin strip

L. A. Ferrari

American Journal of Physics -- March 2009 -- Volume 77, Issue 3, pp. 237 | Cited 1 time

Online Publication Date: Feb 2009

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The scattering of a nonuniform incident wave from a thin conducting cylindrical wire is analyzed. In addition to the usual destructive interference in the diffraction pattern, it is found that there is an additional position of destructive interference that lies close to the central beam axis, within the central diffraction peak. The location of this new point is in general agreement with results given by Ganci. The diffraction calculation by Ganci is extended to include larger values of the ratio of the strip width to beam diameter. The extended theory is found to be in excellent agreement with experiment.
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42.00.00 Optics

Relaxation of Brownian particles in a gravitational field

Halil Saka, Roger D. Bengtson, and Linda E. Reichl

American Journal of Physics -- March 2009 -- Volume 77, Issue 3, pp. 240

Online Publication Date: Feb 2009

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We describe an upper level undergraduate experiment on the time-dependent behavior of a suspension of Brownian particles under gravitational attraction. We employed the Fokker-Planck equation in the strong friction limit and measured the time-evolution of the probability distribution for 1.0 μm diameter latex Brownian particles in water at room temperature and pressure. The experiment provides evidence of the atomic nature of water.
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01.50.Pa Laboratory experiments and apparatus
05.00.00 Statistical physics, thermodynamics, and nonlinear dynamical systems

Demystifying decoherence and the master equation of quantum Brownian motion

John King Gamble and John F. Lindner

American Journal of Physics -- March 2009 -- Volume 77, Issue 3, pp. 244 | Cited 1 time

Online Publication Date: Feb 2009

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Quantum decoherence is a proposed mechanism for the emergence of classical physics from the quantum mechanics. It has been developed extensively in recent years, but is sufficiently technically complicated to discourage widespread understanding. In this paper we provide a gentle introduction to quantum decoherence. We introduce state operators and their density matrix representations to describe composite systems, such as an experiment and its environment. We illustrate how the loss of information about a subsystem can cause a quantum system to appear classical. We first analyze a discrete example of phase randomization, then a Bell state, and finally a continuous system. In the final case we provide an accessible derivation of a major early result of decoherence theory, the master equation of quantum Brownian motion. We conclude by applying the master equation to the decoherence of a simple harmonic oscillator, with results reminiscent of our earlier discrete examples.
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03.65.-w Quantum mechanics

The harmonic oscillator in quantum mechanics: A third way

F. Marsiglio

American Journal of Physics -- March 2009 -- Volume 77, Issue 3, pp. 253

Online Publication Date: Feb 2009

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Courses on undergraduate quantum mechanics usually focus on solutions of the Schrödinger equation for several simple one-dimensional examples. When the notion of a Hilbert space is introduced, only academic examples are used, such as the matrix representation of Dirac’s raising and lowering operators or the angular momentum operators. We introduce some of the same one-dimensional examples as matrix diagonalization problems, with a basis that consists of the infinite set of square well eigenfunctions. Undergraduate students are well equipped to handle such problems in familiar contexts. We pay special attention to the one-dimensional harmonic oscillator. This paper should equip students to obtain the low lying bound states of any one-dimensional short range potential.
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03.65.-w Quantum mechanics

Resistance of a square lamina by the method of images

Lawrence R. Mead

American Journal of Physics -- March 2009 -- Volume 77, Issue 3, pp. 259 | Cited 2 times

Online Publication Date: Feb 2009

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The method of images is applied to find the net resistance of a square lamina whose input/output currents are through point contacts at opposite corners. This application illustrates the rare use of the method of images with an infinite number of image charges.
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41.00.00 Electromagnetism; electron and ion optics

Simulating a toy model of electrodynamics in (1+1) dimensions

A. D. Boozer

American Journal of Physics -- March 2009 -- Volume 77, Issue 3, pp. 262 | Cited 1 time

Online Publication Date: Feb 2009

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We show how to simulate a toy model of electrodynamics in (1+1) dimensions and describe several numerical experiments. The toy model is much simpler than ordinary electrodynamics, but shares many of the same physical features. For example, there are analogs to the electric and magnetic fields, and these fields generate forces between charged particles and support freely propagating radiation. Unlike electrodynamics, however, the toy model is not Lorentz invariant, gives an attractive force between charges of the same sign, and yields a radiation reaction force that depends on the particle velocity.
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02.70.-c Computational techniques; simulations
41.00.00 Electromagnetism; electron and ion optics

Work and energy in inertial and noninertial reference frames

Rodolfo A. Diaz, William J. Herrera, and Diego A. Manjarrés

American Journal of Physics -- March 2009 -- Volume 77, Issue 3, pp. 270

Online Publication Date: Feb 2009

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It is usual in introductory courses of mechanics to develop the work and energy formalism from Newton’s laws. It has been shown how forces transform under a change of reference frame. No analogous study is usually done for the way in which work and energy transform under a change of reference frames. We analyze the behavior of energy and work under such transformations and explicitly show the expected invariance of the formalism under Galilean transformations for one particle and a system of particles. The case of noninertial systems is also analyzed and the fictitious work is characterized. In particular, we showed that the total fictitious work in the center of mass system vanishes even if the center of mass defines a noninertial frame. Some subtleties that arise from the formalism are illustrated by examples.
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47.00.00 Fluid dynamics
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Promoting instructional change via co-teaching

Charles Henderson, Andrea Beach, and Michael Famiano

American Journal of Physics -- March 2009 -- Volume 77, Issue 3, pp. 274 | Cited 2 times

Online Publication Date: Feb 2009

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Physics Education Research (PER) has made significant progress in developing effective instructional strategies, but disseminating the background knowledge and strategies to other faculty has proven difficult. Co-teaching is a promising and cost-effective alternative to traditional professional development which may be applicable in particular situations. We discuss the theoretical background of co-teaching and describe our initial experience with it. A new instructor (Famiano) co-taught an introductory calculus-based physics course with an instructor experienced in PER-based reforms (Henderson). The pair taught within the course structure typically used by Henderson and met regularly to discuss instructional decisions. An outsider (Beach) conducted separate interviews with each instructor and observed several class sessions. Classroom observations show an immediate use of PER-based instructional practices by the new instructor. Interviews show a significant shift in the new instructor’s beliefs about teaching and intentions of future use of PER-based instructional approaches.
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01.40.Fk Research in physics education
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Wick calculus using the technique of integration within an ordered product of operators

Hong-yi Fan and Cui-hong Lü

American Journal of Physics -- March 2009 -- Volume 77, Issue 3, pp. 284

Online Publication Date: Feb 2009

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We show that the connection between Wick ordered polynomials and Hermite polynomials derived by Wurm and Berg by an inductive method can be directly and concisely obtained using the technique of integration within an ordered product of operators (IWOP).
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03.50.-z Classical field theories
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Engines of Discovery: A Century of Particle Accelerators

Andrew Sessler, Edmund Wilson, and Catherine Westfall, Reviewer

American Journal of Physics -- March 2009 -- Volume 77, Issue 3, pp. 287

Online Publication Date: Feb 2009

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

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American Journal of Physics -- March 2009 -- Volume 77, Issue 3, pp. 287

Online Publication Date: Feb 2009

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