April 2022 AJP coverApril 2022 Issue,

Volume 90, No. 4


Marinated eggs: An engaging quantitative demonstration of diffusion featured


Marinated or pickled eggs are enjoyed in cultures across the world, and recipes for these eggs use diffusion to saturate the egg white of a hard-boiled egg with sauce. Inspired by the marinated egg, this experiment demonstrates diffusion in an easy and quantitative way. Peeled hard-boiled eggs are placed in a dye solution, and the penetration distance of the dye into the egg white is measured as a function of time using image processing. The penetration distances are consistent with the expected dependence on the square root of time, and the diffusion of the dye occurs faster at higher temperatures as expected. This experiment provides a new way to demonstrate diffusion-based mass transfer visually and to make a connection between physics and culture.



In this issue: April 2022 by Joseph Amato, John Essick, Claire A. Marrache-Kikuchi, Beth Parks, Donald Salisbury and Todd Springer. DOI: 10.1119/5.0089096


Radiated energy and momentum for time-dependent dipoles by Kirk T. McDonald. DOI: 10.1119/5.0088991

Electricity + Relativity → Magnetism by John Houlihan. DOI: 10.1119/5.0086631

A short pre-history of quantum gravity by S. Deser. DOI: 10.1119/5.0080405


Updating our language to help students learn: Mechanical energy is not conserved but all forces conserve energy by American Journal of Physics 90, 251 (2022); https://doi.org/10.1119/5.0067448
A call to change the language we use when teaching introductory mechanics.


Universal functions by Sanjoy Mahajan. DOI: 10.1119/5.0088966
This month’s Back of the Envelope column illustrates how plotting the right combination of variables can beautifully illustrate physical laws.


Balloon-borne two-channel infrared spectral photometer for observation of atmospheric greenhouse effect by undergraduates by Gerard T. Blanchard, Fawaz A. Adesina, William Cole Belkwell, James R. Dyess, Victoria A. Frabbiele, Conor S. McGibboney and Ryan D. Rumsey. DOI: American Journal of Physics 90, 256 (2022); https://doi.org/10.1119/10.0009284
The greenhouse effect is a crucial parameter of climate change, but it is difficult to exhibit in tabletop experiments. This paper proposes a student project that, by launching Arduino-based radiation sensors in a balloon, measures that the radiation emitted by the Earth and its atmosphere towards space has an effective temperature that decreases with altitude. They also measure the effects of water and CO2 absorption. This undergraduate project could be adapted for ground-based experiments and can also serve as a practical illustration of Planck’s law.

The analog computer: Beyond the museum artwork, a tool for studying linear and nonlinear systems by Marcello Carlà. DOI: 10.1119/10.0009634
There was a time when physicists would argue whether analog or digital computing would win out as the more useful technology. Remember, in 1969, NASA used analog and hybrid (analog computers controlled by digital electronics) computers for simulations and (some) flight control in the Apollo 11 mission! This era is now gone, but analog computers are still an interesting pedagogical tool, as this manuscript shows. In particular, educators can introduce undergraduate students to operational amplifiers-based electronic circuits that constitute the building blocks for analog computing: the summing node, the integrator, and the multiplier module. From there, solutions for linear and non-linear oscillators can be derived, thus relating electronic circuits to more general physics problems.

How physics textbooks embed meaning in the equals sign by Dina Zohrabi Alaee, Eleanor C. Sayre, Kellianne Kornick and Scott V. Franklin. DOI: /10.1119/10.0009096
Experts in physics may take for granted many steps in the problem-solving process that have become deeply ingrained after years of practice.  These concepts may not be part of a traditional physics course, but, nevertheless, they might need to be taught.  One such concept, often taken for granted, is the meaning of the equals sign.  In this article, readers will find a categorization scheme of many possible meanings that are encoded into an equals sign in physics.  This article will be of interest to educators wanting to gain a fresh perspective on the difficulties their students may face when trying to interpret mathematical formulae.

Simulation led optical design assessments: Emphasizing practical and computational considerations in an upper division physics lecture course by Vincent M. Rossi. DOI: 10.1119/5.0064138
Computation-based simulations in an optics course allow students to gain practical experience in optics at the same time that they develop coding skills. The author has developed a sequence of computational exercises that take students from an introductory level (in both optics and coding) to the design and simulation of optical systems such as spectrometers and polarization-imaging microscopes. These exercises are described in the paper, and the author shares the full set of assignments in the accompanying online supplementary material.

Continuous gravitational waves in the lab: Recovering audio signals with a table-top optical microphone by James W. Gardner, Hannah Middleton, Changrong Liu, Andrew Melatos, Robin Evans, William Moran, Deeksha Beniwal, Huy Tuong Cao, Craig Ingram, Daniel Brown and Sebastian Ng. DOI: /10.1119/10.0009409
In the past few years, we have all been thrilled by the “chirps” detected by LIGO and other gravitational wave (GW) observatories. These tiny signals are generated by binary systems containing black holes and/or neutron stars in the brief moments before their coalescence. The same observatories are also searching for continuous GWs, signals that are nearly constant in frequency and persist for years, emitted by non-spherical spinning neutron stars. The authors describe a tabletop Michelson interferometer–a mini-GW detector–that uses sound vibrations to perturb its interference pattern in a manner similar to GW detection. They then introduce the Viterbi algorithm, a signal processing technique used by GW observatories to detect signals that drift slowly in frequency, and demonstrate its effectiveness using their tabletop apparatus. Finally, the authors review a number of signal-processing techniques, employing their apparatus as an “optical microphone” to demonstrate each technique’s effectiveness in recovering speech and music in noisy environments. The apparatus can be used as a demonstration of GW detection for non-specialists, or, with an added emphasis on signal processing, in physics, engineering, or cross-disciplinary classes.

Energy-mass equivalence from Maxwell equations by Alejandro Perez and Salvatore Ribisi. DOI: 10.1119/10.0009156
Einstein's equation expressing the relationship between mass and energy, E = mc2, is perhaps the most famous equation in physics.  Historically, the relationship between mass and energy predated the equivalence principle, one of the cornerstones of general relativity.  In this article, the equivalence principle is used to derive Einstein’s most famous equation.  Even though it did not come about this way historically, the exploration of this connection can still be pedagogically useful for those interested in special relativity, general relativity, and the connection between the two.


Relativistic spin-0 particle in a box: Bound states, wave packets, and the disappearance of the Klein paradox by M. Alkhateeb and A. Matzkin. DOI: 10.1119/10.0009408
This informative relativistic supplement to an introductory undergraduate course in quantum mechanics introduces the Klein-Gordan wave solution as a single particle wave function. With the interpretation of negative energy states as representing anti-particles, one gains a recognition of the scalar product as representing charge density, and this constitutes a first step toward quantum field theory. Indeed, the Klein paradox itself, with its production of an amplified current incident on a single potential energy barrier, has as yet neither a sound theoretical basis nor experimental grounding regarding the behavior of bosons confined to a classical potential well. In addition, students will appreciate the multiple scattering analysis that leads to a classical particle interpretation.


Phase plot of a gravity pendulum acquired via the MEMS gyroscope and magnetic field sensors of a smartphone by T. Splith, A. Kaps and F. Stallmach. DOI: 10.1119/10.0009254
With a smartphone serving as the bob of a gravity pendulum, the pendulum’s time-dependent angular displacement and velocity are produced from data acquired from the phone’s gyroscope and magnetometer sensors via the phyphox app. Experimental phase-space plots from the analysis of these data are presented, along with fits to the expected theoretical curves. This experiment is suitable as a lecture demonstration as well as an instructional laboratory experiment. Detailed instructions on how to adopt the experiment are provided in the supplementary material.


Marinated eggs: An engaging quantitative demonstration of diffusion by Carson Emeigh, Hyeonggeun (Luke) Bak, Dilziba Kizghin, Haipeng Zhang and Sangjin Ryu. DOI: 10.1119/5.0062178
Many cultures feature foods in which a flavored sauce is infused into hard-boiled eggs. The authors use eggs soaked in red food coloring to show that this process follows Fick’s law of diffusion, creating a fun and engaging demonstration or laboratory exercise for undergraduates.

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