Volume 62, Issue 3, March 1994
 Editorial
 Papers


Suppose Newton had invented wave mechanics
View Description Hide DescriptionIt is difficult to understand quantum mechanics. A major reason for this is that people do not realize that classical mechanics can be very well described by quantum mechanics. It would all have been much easier if Newton had not developed classical mechanics from the equation relating force, mass, and acceleration of a particle, but had started from a simple form of the Schrödinger wave equation. The equation F=ma could just as well have waited for its derivation from quantum mechanics by Paul Ehrenfest in 1927.

Third electromagnetic constant of an isotropic medium
View Description Hide DescriptionIn addition to the dielectric and magnetic permeability constants, another constant is generally needed to describe the electrodynamic properties of a linear isotropic medium. We discuss why the need for the third constant arises and what sort of physical situations can give rise to a nonzero value for it. This additional constant, which we call the ‘‘activity constant’’ and denote by ζ, can explain optical activity and other phenomena from a purely macroscopic and phenomenological point of view.

Suppression and restoration of constants
View Description Hide DescriptionGiven a set of physical equations containing one or more positive dimensionally independent constants, one can suppress the constants by setting them equal to unity, operate mathematically with the resulting simplified equations, and at the end restore the constants in the final equations. A simple explanation of how and why this method works, and six examples of the application of this method are given. The first example clarifies certain details of the mechanism behind the method. The remaining examples illustrate the utility of the method in the determination of the orbits of a particle in an inverse square attractive force field, the effect of the Coriolis force on the motion of a freely falling particle, the vertical ascent of a rocket in a uniform gravitational field, the nature of a plane electromagnetic wave propagating in a medium of constant permeability and permittivity, and the motion of an electron in a Bohr atom.

Singing corrugated pipes revisited
View Description Hide DescriptionA long corrugated tube open at both ends sings notes which depend on the flow velocity of air flowing through the tube. The notes it sings are natural harmonics of the tube. In 1974, Crawford suggested an explanation for this: A given note will sing when the flow velocity is such that the ‘‘bump frequency’’ equals the frequency of the note, provided also that the flow velocity is sufficiently high to induce turbulent flow. He suggested two theories to explain the singing in terms of turbulence. One assumed that the onset of turbulence agrees with the classic Reynolds number for smooth tubes (R _{smooth}≊2000) in which the characteristic length of the object that has air flowing in is equal to the diameter. The second assumed the characteristic length of the object was equal to the distance between the corrugations. Crawford reported having good agreement between the classic diameter‐induced turbulence theory and experiment for some pipes. However, for other tubes he observed singing at Reynolds numbers that were much smaller than the classical result of 2000. For these, he could not establish if he was observing corrugation‐induced turbulence. (He stated he did not have sufficient pipes.) After looking at a variety of tube diameters and corrugation lengths, we also observed (as Crawford reported) that some of the data agreed with the classic diameter‐induced turbulence, and some did not. Ironically, the hypothesis Crawford introduced (and rejected) as an alternative possibility seems to fit ALL of our data quite well. A new Reynolds number associated with the onset of turbulence for corrugated pipes is presented: R _{corr}≊500.

Time‐delay oscillator and instability: A demonstration
View Description Hide DescriptionA harmonic oscillator where the force is dictated not by the current position but the position at a slightly earlier time is considered and shown to be unstable. This and closely related systems are called time‐delay oscillators and the instability, when it is present, is called a time‐delay instability. A simple, easy to construct demonstration is presented and analyzed. A discussion of the robust nature of the instability is also given.

Teardrop and heart orbits of a swinging Atwood’s machine
View Description Hide DescriptionAn exact solution is presented for a swinging Atwood’s machine. This teardrop–heart orbit is constructed using Hamilton–Jacobi theory. The example nicely illustrates the utility of the Hamilton–Jacobi method for finding solutions to nonlinear mechanical systems when more elementary techniques fail.

The image of the physicist in modern drama (Part 2)
View Description Hide DescriptionIn an earlier paper, we reviewed a number of post‐World War II plays which focused on the role scientists, and more particularly physicists, ought to play in modern society. In this article we continue this type of review, concentrating on the plays of Charles Morgan, Archibald MacLeish, Carl Zuckmayer, and Tom Stoppard, using Thomas Shadwell’s classic play The Virtuoso to set the stage for the more modern plays. These plays portray, in the eyes of the playwrights, something of the image of science as a way of gaining knowledge about nature, but focus more strongly on the difficult choices faced by scientists in a world in which the social implications of scientific discoveries have become almost overwhelming.

Computer modeling of resonance scattering in the time domain
View Description Hide DescriptionMicrocomputer generation of motion pictures illustrating solutions of Schrödinger’s time‐dependent equation is described. The technique is used to model the resonance scattering of a Gaussian wave packet by a spherical step‐potential well. The formation of transient resonance states is observed, and the decay times correlated with the widths of the resonances.

Brewster’s angle and optical anisotropy
View Description Hide DescriptionBrewster’s angle has been determined for a transparent oriented anisotropicmaterial. For simple orientations of the material a polarizing angle can be found, but the propagation vectors for the reflected and refracted light are not perpendicular at this angle of incidence. In addition, Brewster’s law, n’=tan θ, does not apply in this case. For an arbitrary orientation of the material there is usually no angle of incidence that produces linearly polarized reflected light. These results can be understood by considering the direction of oscillation of induced dipoles within the material.

On presenting wave–particle duality using a simulated detector for multiple slit diffraction
View Description Hide DescriptionUsing a computer program and monitor to simulate a detector for multiple slit diffraction provides a realistic illustration of what is meant by wave–particle duality. An example program is described; results are presented with figures.

Nonrelativistic calculation of the radiation emitted by a pair of identical particles
View Description Hide DescriptionThe calculation of the electromagnetic radiation produced by a pair of nonrelativistic charged particles presents an interesting difficulty in the case where the net dipole moment of the system vanishes. One apparently attractive method of solution fails dramatically for the classic problem of two electrons in relative circular motion. The reason for the failure is explained, for this and other systems.

Dust off the neutron howitzer to teach nuclear physics!
View Description Hide DescriptionA wide variety of topics in nuclear physics can be taught in the undergraduate laboratory using just a few metallic samples for activation in a neutron howitzer. Rather than scorned for its low neutron flux, the neutron howitzer can be appreciated for its safety in the physics teaching laboratory and its usefulness in conjunction with high‐resolution gamma spectroscopy.

Newton’s pail in Einstein’s lift
View Description Hide DescriptionThe classic Newton’s pail experiment performed in a freely falling lift is discussed.

Numerical integration of Newton’s equations including velocity‐ dependent forces
View Description Hide DescriptionNumerical integration routines designed for introductory physics courses, such as the last‐point approximation and the second Taylor approximation, are incompatible with velocity‐dependent forces. A general purpose routine which handles resistive, Coriolis, and magnetic forces, as well as conservative forces, is obtained by combining the fundamental Euler method with Richardson extrapolation. Further, this Euler–Richardson method is almost as efficient as the last‐point approximation and the second Taylor approximation for simple central force problems and is more efficient for difficult problems, such as Earth–Moon orbits.

Compton scattering, the electron mass, and relativity: A laboratory experiment
View Description Hide DescriptionCompton scattering in a semiconductor detector is used to ‘‘discover’’ the relativistic relation between energy and momentum and to demonstrate the dependence of p, E and γ on β. The motivation is to measure the (rest) mass of the electron, and this can be done to within 1 keV with a commonly available set of gamma ray sources. To determine precisely where the Compton edge occurs in a spectrum, a Monte Carlo calculation of detector response is described which also helps the student to understand the physics of the detection process.

Dispersion‐free linear chains
View Description Hide DescriptionGeneral formulas are given for the masses and spring constants of one‐dimensional finite chains with linear dispersion relations, examples of which were given by Herrmann and Schmälzle in 1981 in their discussion of a well‐known collision apparatus. The mathematical similarity to the problem of a Boson in a constant magnetic field is shown. The explicit formulas make a study of the continuum limit possible. This is shown to be related to the system of uniform rods studied by Bayman in 1976. Examples are given of chains with quadratic dispersion relations. Resonances that give singularities in the interaction time are discovered in certain chains of elastic spheres.
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 Notes and Discussions


Comment on ‘‘Wakes and waves in n dimensions,’’ by H. Soodak and M. S. Tiersten [Am. J. Phys. 61, 395–401 (1993)]
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On the derivation of the formula for relativistic momentum
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The magnetic analogue of the inverted pendulum
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