American Journal of Physics, February 2024February 2024 Issue,

Volume 92, No. 2

Easy method to establish the dispersion relation of capillary waves on water jets

A simple, intuitive, and low-cost setup for generating and measuring capillary waves is presented enabling a precise determination of the dispersion relation for a cylindrical water jet. By setting the phase velocity and measuring the wavelength of capillary waves directly, this method provides an intuitive way for students to understand the dispersion relation of a cylindrical water jet. The setup produced measurements of wavelength versus phase velocity over a broader range of values than earlier work. The resulting data are generally consistent with earlier results but show an error of up to 15% at both the higher and lower end of the measured range of wavelengths compared to the theoretical dispersion relation of cylindrical water jets. For the shorter wavelengths, the deviation is in the opposite direction from that of earlier work.


In this issue: February 2024 by John Essick; Claire A. Marrache-Kikuchi; Beth Parks; B. Cameron Reed; Donald Salisbury; Keith Zengel. DOI: Am. J. Phys. 92, 85–86 (2024)


From sucking worms to Windkessel: The physics of an early eighteenth century firefighting device by Don S. Lemons; Trevor C. Lipscombe. DOI: Am. J. Phys. 92, 87–92 (2024)
The authors present a compelling history of firefighting devices that leads to far-ranging applications including the heart-aorta blood delivery system and modern groundwater pumps. Their model, which relies on simple assumptions, the ideal gas law, and Bernoulli's principle, makes the physics of output streams an accessible topic for undergraduate lectures and labs. Instructors can tailor the information to a variety of student interests.

Easy method to establish the dispersion relation of capillary waves on water jets by Wout M. Goesaert; Paul S. W. M. Logman. DOI: Am. J. Phys. 92, 93–99 (2024)
Phase velocity and dispersion relationships are challenging concepts for students. This experiment provides an opportunity for students to measure the dispersion relationship for capillary waves that are formed when a jet of water hits an obstacle. These waves can be photographed and characterized, and the wavelength and speed can be varied by changing the distance to the obstacle.

Coriolis acceleration and critical slowing-down: A quantitative laboratory experiment by R. Mathevet; P. Marchou; C. M. Fabre; N. Lamrani; N. Combe. DOI: Am. J. Phys. 92, 100–107 (2024)
Students often study a pendulum in physics laboratories, obtaining fairly predictable results. However, if a pendulum is placed on a turntable, the results are much more interesting: Students can measure the Coriolis acceleration and also observe a pitchfork bifurcation. This paper shows you how. Appropriate for undergraduate mechanics classes, as well as for advanced statistical physics classes or courses on phase transitions. A video abstract accompanies the online version of this paper.

Periodic strings: A mechanical analogy to photonic and phononic crystals by R. S. Pitombo; M. Vasconcellos; P. P. Abrantes; Reinaldo de Melo e Souza; G. M. Penello; C. Farina. DOI: 10.1119/5.0094212
In this paper, the authors propose a classical analog to the propagation of light in 1-D photonic crystals or of phonons in 1-D phononic crystals. The transmission of a mechanical wave through a periodic arrangement of strings with different linear mass densities is studied theoretically by the transfer matrix method. The frequencies of the propagating wave are analogous to the crystal's electronic energies, and the frequency gaps where there is no transmission through the periodic string are akin to energy bandgaps in the quantum counterparts. The authors calculate the effect of changing the relative string mass densities, and thus simulate a change in the scattering of the mechanical wave. This paper proposes an example of a macroscopic mechanical system that can serve as proxy for a microscopic quantum system. Experimentalists are invited to report on its implementation. Appropriate for undergraduate advanced mechanics class, in relation with condensed matter physics.

Eigenmodes of fractal drums: A numerical student experiment by Veronica P. Simonsen; Nathan Hale; Ingve Simonsen. DOI: 10.1119/5.0140853
In 1966, the Polish mathematician Mark Kac published the seminal and influential paper: “Can one hear the shape of a drum?” One response of researchers to this question has been to study the modes of fractal drums. This paper shows how that topic can be incorporated into a computational physics course, providing a modeling challenge to which students respond enthusiastically.

Visualizing non-adiabatic quantum dynamics and photo-excitation processes on Excel by Erica L. Fultz; Jovan Gras; Michael Messina. DOI: 10.1119/5.0139464
In physical chemistry, the time-dependent Schrodinger equation is used to model the dynamics of the motions of nuclei in diatomic molecules, exchange of an atom from a donor molecule to an acceptor one, and also photo-excitation processes wherein a diatomic molecule is excited from a ground electronic state to an excited state due to absorption of a photon from an outside laser field. This paper describes a suite of Excel spreadsheet modules for simulating these processes. Several examples are detailed and an extensive set of student exercises is offered. Appropriate for advanced quantum mechanics/physical chemistry students.

Adiabatic invariance and its application to Wien's complete displacement law of blackbody radiation by Don S. Lemons; William R. Shanahan. DOI: 10.1119/5.0158187
Wien's displacement law is usually treated as a relationship between the peak of the spectral energy distribution of blackbody radiation and the absolute temperature T. However, this is only part of the story; a more complete version of the law relates the energy density of the radiation in a small range of frequencies (n, n + dn) to a function of the ratio n/T. In this paper, the authors describe the history of the more complete version and derive it by considering two adiabatically invariant quantities: one involving a finite range of frequencies of the radiation and another involving the behavior of waves reflected from a slowly-moving boundary of the system. This analysis brings the derivation of the displacement law to a more thermodynamic basis (as opposed to quantal), and is also applicable to an ideal gas and the acoustic waves of a Debye solid. Appropriate for advanced thermodynamics students.

Ehrenfest paradox: A careful examination by Jitendra Kumar. DOI: 10.1119/5.0153190
Instructors even in introductory physics, employing simply Lorentz transformations, will benefit from this resolution of the over a century old Ehrenfest paradox concerning the rotation of a solid ring about its central axis.


A simple state-of-the-art spectrometer for student labs: Cost-efficient, instructive, and widely applicable by Andreas Eggenberger; Tomasz Smolenski; Martin Kroner. DOI: 10.1119/5.0164044
This paper describes a Czerny-Turner spectrometer designed for use in an undergraduate instructional laboratory course. The instrument is constructed from commercially available components, including an optical fiber for light input and a CCD for light detection. Each of the spectrometer's components is accessible to students, producing a build-it-yourself setup that illustrates the fundamentals of spectroscopic measurements. The instrument's resolution and spectral range are characterized and several examples of student applications are presented, including acquisition of spectra for the sodium doublet, the Balmer series, and Fraunhofer absorption. Other possible explorations made possible by the resolution and flexibility of this instrument are suggested. This work will be of interest to instructors of instructional laboratory courses in modern physics and intermediate-level optics.


Developing a low-cost experimental apparatus to observe the Tyndall effect using an Arduino and 3D printing by Luiz Américo Alves Pereira; Rozane de Fátima Turchiello; Sergio Leonardo Gómez. DOI: 10.1119/5.0146499
The Tyndall effect (scattering from suspended solids) gives color to blue eyes and opalescent gemstones. Instructors looking for a way to introduce students to this effect while simplifying the measurement process will appreciate this paper, which describes the use of a 3-D printed holder to aid experimenters. Supplementary material includes the files that will allow readers to easily adopt these plans.

Photographing a meter stick moving at relativistic speeds by Len Zane. DOI: 10.1119/5.0167793
For instructors trying to avoid misconceptions in special relativity, this Note provides a scenario that displays length contraction without the need to worry about clock synchronization or speed-of-light delays. It could easily be turned into a guided exercise for students who could then be led to discover the result on their own.

Surface charge and surface current densities at material boundaries by Richard Marchand. DOI: 10.1119/5.0164442
Physics instructors know that electric fields of polarized materials can be found using bound surface and volume charges; similarly, magnetic fields of magnetized materials can be found using bound surface and volume currents. While the bound volume charges and currents are easily understood to result from the divergence of the polarization and the curl of the magnetization, the bound surface charges and currents are less easily understood. This paper considers these surface charges and currents as resulting from discontinuities of the polarization and magnetization at the surface. It will help instructors answer student questions about these familiar calculations.


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