II IPT Conference Proceedings

International Physicists' Tournament IIIPT Conference Proceedings Eidgenössische Technische Hochschule (ETH) Zürich, 2024 IIIPT Conference Proceedings Eidgenössische Technische Hochschule (ETH) Zürich, 2024 by Executive Committee of the International Physicists’ Tournament along with authors Maressa Pimenta Sampaio, Giovanna Fernandes do Valle, Iason Kazazis, Renan Gomes Alvim, Pietra Dominicini Zanni, Lucas Nogueira Roberto, Viktor Sundström, Ihor Sachok, Seyedeh Zahra Hosseini, Penelope Pouli, Nicolai Christian Kongstad, Lucas de Alexandri Dantas Heck, Malli Segoli, Daryna Sych, Vinícius dos Passos de Souza, Wiktor Kalinowski,Michał Puza, Filippos Typas, Oscar Ernesto Angulo Flores, Mahan Fallahpour, Amin Reza Mahmoodi, Angelopoulou Eleni-Amaranta, Griffin Hiscoke, Bruno Siqueira Eduardo, Ivan Prearo, Mateusz Winiarski, Wiktor Zantowicz, Alexandros Desylas, Anna Krasylnikova. Executive Committee: Anastasiia Vasylchenkova, Alberto Rolandi, Kyrylo Gerashchenko, Matheus A.S. Pessôa, Nikolay Lysenko, Vladimir Vanovskiy, Mathieu Suter, Maja Milas, Aakash Bhat, Christos Andrikopoulos, Rosty Bruce, Jeanne Bernard, Joachim Hermansen, Didar Sedghi, Alisa Miloglyadova E-mail us at [email protected] Visit the IPT website at iptnet.info Cover: X ETH Zurich Style: TU Delft Report Style, with modifications by Matheus Pessôa IPT Conference Proceedings Preface by our president Dear IPT Community, it became a good tradition to gather the solutions of the IPT problems, have fun and stimulating discussion at the IPT Conference and publish the book of abstracts. We know very clearly how much efforts and enthusiasm you guys are putting into solving the problems, running the experiments, analysing hours of videos, deriving monstrous equations. This all makes the IPT a unique learning experience. This bookof abstracts is another way from us to give your efforts an academic weight, and to give you a safe space for working on it - for some of our participants, the IPT Conference may be their first experience of conference participation. I am grateful to all the contributors who filled the book with their diverse contributions. See you next year! All the best, Anastasiia Vasylchenkova President of the IPT November 2025 i IPT Conference Proceedings A word to the students Dear IPT participants, Welcome to the second edition of the Conference Proceedings of the IPT! This year we had a record of participation at the conference, which reflects also the number of abstracts that were included here. When we first started the conference, we had no idea how big it would become„ but it shows the dedication and passion for solving very peculiar physics problems such as building a galton board, determining how good a cachaça is through sound (a trick that even being Brazilian I did not know of), or predicting the which egg will win an egg fight (also one of the curious things I learned this year). Thanks a lot for all contributions! Matheus Azevedo Silva Pessôa Editor of the IPT Conference Proceedings and Member of the Executive Committee of the IPT November 2025 ii IPT Conference Proceedings Contents Preface i A word to the students ii 1 Exploring the Boundaries of the Central Limit Theorem: An Experimental and Theoretical Investigation of the Galton Board 3 2 Non-gaussian Controllable Galton Board Distributions through Modelling with a Single Metaparameter 4 3 Solution of the Galton board problem with three different approaches 5 4 Jumpy Hoop 6 5 Probing the motions of a spring under current 7 6 Qualifying the Damped Oscillation of Acoustic Bubbles. 8 7 Experiment and simulation of damping in alcohol solutions 9 8 Tuning into Spirits: The Sound of Quality Liquor 10 9 Formation of PVC cement droplets 11 10 Salty shapes and Swiss cheese 13 11 A theoretical model for the echo from the Chichen Itza pyramid 14 12 Echoes from staircases calculation by convolution-scattering 15 13 The Enigma of the Chirping Echo: Unveiling the Acoustics of Chichen Itza’s Pyramid 16 14 Decoding Shadows 17 15 Poisson spot 18 16 A geometric approach to diffraction 19 17 The Bright Spot 20 18 Study of the Arago-Poison spot 21 19 Crack Conundrum: Exploring Factors Influencing Success in the Traditional Game of ’Egg Tapping’ 22 20 Egg Fight Predictions: A Resonant Frequency Analysis method to determine the winner of an egg fight 23 21 Sound analysis of unrolling tape 24 22 Preliminary investigations into surface anti-bubbles 25 23 Anti-bubbles formation and lifetime 26 24 Egg Fight 27 iii IPT Conference Proceedings The IPT Problems During the competition, we saw solutions of all 17 IPT problems. In these proceedings, we present abstracts from 10 of these problems, which are listed below. Galton board Dropping a set of beads on a board with evenly distributed pegs results in a binomial distribution. Is it possible to generate other kinds of distributions by varying some parameters (pegs size, pegs distribution, bead format, etc.)? Is it possible to achieve a distribution that does not obey the central limit theorem in an i.i.d. scenario? What happens to the distribution when one makes the board vibrate? Jumpy Hoop Given enough angular momentum, a hoop with a mass attached to it may demonstrate a jumping motion when it is rolling. Explain the phenomenon and how it depends on the relevant parameters. Is it possible to reproduce this behavior with any unbalanced mass distribution on a wheel? What happens when one changes the profile of the ground? Can you add a mechanical contraption (that will not touch the ground) to the hoop to increase the maximal height of the jump? Solenoid Resonance Consider a helicoidal spring hanging vertically with a mass attached to it as a solenoid. If one lets current flow through the spring, it creates a magnetic field. How can one influence the motion of the spring by changing this current? What happens if we put this system in an RLC circuit (where L is our spring) with AC current? What kind of resonant phenomena and energy transfer between the mechanical and electromagnetic modes can be achieved? Alcohol sound check Some distilleries in Brazil praise their product’s quality by the distinct sound it makes when the bottle is hit after being quickly turned upside down. Investigate the phenomenon. Why does the effect not work with alcoholic carbonated drinks? What other liquids will maintain this “damping” effect for longer? PVC cement droplets PVC cement is a material used in plumbing to solder PVC pipes together. PVC cement droplets have been observed to spin when dropped in water. Explain the physical mechanisms that cause the peculiar motion of the droplets. Study how the shape of the droplets impacts their rotation. Can you create droplets that propel across the water instead of rotating? Maximize their rotational and translational motion. Salty shapes In some deserts, such as Death Valley, one can see salt polygons that have formed through the evaporation of salty water. Investigate and explain the phenomenon. Reproduce the phenomenon in the lab. Which two dimensional pattern can one obtain in such an experiment? What is the size of the smallest polygon you can obtain? Peculiar echo The combination of a clap and the massive pyramid (Chichen Itza, Mexico) gives rise to a mysterious sound called “Quetzal tail”, as shown in the video. Investigate the phenomenon, find the necessary conditions to create it, and reproduce it. 1 IPT Conference Proceedings The bright spot There is a famous phenomenon in wave optics called the Arago-Poisson spot where a bright spot is created in the middle of the shadow of a spherical object when one shines coherent light on it. By shining the light on other types of solids (e.g. cubes, cylinders, etc.) one gets different patterns to appear in the shadow of the object. What information about the geometry of a solid can be obtained by analyzing the pattern in its shadow? Egg fight Egg tapping is a traditional game where two players hold a boiled egg. Each player hits the other player’s egg with their own, as shown in the video. The player whose egg has cracked loses the game. Devise a non-invasive method to predict the winning egg among the given two. Improve the prediction with invasive examination methods. Unrolling tape When unrolling a roll of adhesive tape, a loud sound can be produced. Explain the physics of the sound emission. Find ways to maximize and minimize the noise. Anti-bubbles Fill a container with water with decreased surface tension. Then drop a droplet of regular water into the container (very slowly). The droplet will create a so-called “anti-bubble”. Investigate the phenomenon. Maximize the size and lifetime of an anti-bubble. Are these quantities related? IPT Conference Proceedings 1 Exploring the Boundaries of the Central Limit Theorem: An Experimental and Theoretical Investigation of the Galton Board Iason Kazazis, Greece The Galton board is a simple yet effective device that demonstrates how the Central Limit Theorem applies to a physical system and allows for the visualization of discrete probability distributions, such as the binomial distribution, which approximates the normal distribution. This work investigates the physical parameters of the board that determine the final distribution of the beads, aiming to generate non-normal distributions. We focus on the features of the distributions in order to examine if the Central Limit Theorem applies when certain conditions are met. We further explore the effects of a vibrating board. In order to study the motion of the objects on the board, an original, problem-specific notation has been developed based on the random walk stochastic process. Two different experimental setups were constructed to perform tests with changing variables and a vibrating motion which were compared to numerical simulation results. The experimental and theoretical results as well as future study prospects are discussed. 3 IPT Conference Proceedings 2 Non-gaussian Controllable Galton Board Distributions through Modelling with a Single Metaparameter Griffin Hiscoke, Sweden To statistically observe the resulting distribution of balls dropping through a non-ideal Galton Board, the underlying mechanical processes must be modelled and approximated. This study proposes a parameter which summarises the effects of a range of factors such as elasticity, shapes, spacings and sizes, and allows for fast determination of the resulting distribution. This is done by considering the probability of a ball continuing to move in the same direction when it descends a layer and hits a peg. The parameter, and by extension the behaviour of the full board, can be measured by conducting a low number of experiments on a subset of the board consisting of only 3 pegs. The simplification is then applied to model a real-world board and used to generate non-uniform peg distributions which provide controllable non-gaussian resulting distributions. Physical experiments show the model to have a smaller inaccuracy than the human error caused by placing pegs by hand. Although the parameter depends on a wide range of properties, we elected to vary it through changing the horizontal spacing between peg columns. Further studies would include exploring the limits of the simplification, as well as reducing human error in constructing physical boards. Additional experiments could allow for predicting the parameter value for different board parameters without conducting experiments on the specific board. 4 IPT Conference Proceedings 9 Formation of PVC cement droplets William Castillo Cabrera, Mexico When drops of PVC cement are deposited on water, they will start spinning with chaotic movement. To characterize this phenomenon, we used different methods leading to the conclusion of water tension being the main reason. Therefore, when the solvents of the cement evaporate, between the tension layer and the surface of the PVC droplet, there is an accumulation of solvent that ends breaking up thus leading to the chaotic movement. 11 IPT Conference Proceedings Figure 9.1: Experimental images of the formation of different types of PVC cement droplets, in blue for higher contrast. IPT Conference Proceedings 10 Salty shapes and Swiss cheese Mateusz Winiarski, Wiktor Zantowicz, Poland (Krakow) It is known, that salty shapes create pattern known as Voronoi shapes. In our presentation, we will show a Voronoi-like pattern inspired by Swiss cheese, that matches provided theory as well as results seen in nature. 13 IPT Conference Proceedings 11 A theoretical model for the echo from the Chichen Itza pyramid Bruno Siqueira Eduardo, Brazil When one claps in front of the Chichen Itza pyramid, an interesting echo is generated. After the investigation of some qualitative aspects of the phenomenon, we were able to isolate the most important parameters that contribute to the resultant sound. They motivated a set of reasonable assumptions to the problem, allowing the development of a theoretical model whose inputs are solely the duration of the clap, the speed of sound, the distance to the pyramid and the geometry of its main staircase. The output of the model is a simple analytical expression that accuratly reproduces the ”peculiar” features present in the spectrogram of the echo, with no need to fit any parameters. 14 IPT Conference Proceedings 12 Echoes from staircases calculation by convolution-scattering Ivan Prearo, Brazil The peculiar echo produced by the El Castillo pyramid has been studied and reproduced both mathematicall and experimentally in situ. The main cause of the echo was found to be the geometry of an observer claping their hands at a reasonable distance of the bottom of the pyramid. Two modelling approaches give very similar results in accuracy with different degrees of detail: construction interference between echos from consecutive steps; and the staircase as a diffraction grid with varying step sizes. The echo effect was observable in 4 separate UNICAMP staircases, which were measured and had their echoes calculated using a convolution-scattering model [1] in order to compare experiments and theory. The frequency spectrum found from the models agreed with the aquired experimental data. Using the construction interference model, it is possible to have a rough first estimate for the frequency curve for the echo of any staircase. This was used to verify the possibility of a lab-scale experiment, with milimiter-sized steps. Since the frequencies found were in the order of 115kHz, way above the human hearing limits, this experiment was discarded [4]. 15 IPT Conference Proceedings 13 The Enigma of the Chirping Echo: Unveiling the Acoustics of Chichen Itza's Pyramid Amin Reza Mahmoodi, Mahan Fallahpour, Seyedeh Zahra Hosseini, Iran In this research the intriguing phenomenon of the ”chirping echo” produced by the Great Pyramid of Chichen Itza, is investigated. When a clap resonates against the structure’s steps, a sound akin to a quetzal bird’s call emerges. By meticulous diffraction simulations, the research tackles the question of how the architectural design of the pyramid shapes the echo into a series of chirps. The repetitive pitch phenomenon analysis reveals a critical finding: the frequency of the returning sound is independent of the initial clap and instead, it is entirely due to the intricate geometric configuration of the pyramid itself. Two prominent models are used to explain this fascinating acoustic interaction: the Lubman torsional scattering model and the Declercq diffraction model. The Lubman model depicts the clap-echo process as a linear system that remains constant over time. However, its results indicate a dependence of the echo on the random spectrum of the initial sound, which contradicts the observed independence of frequency from the source. In contrast, the Declercq diffraction model offers a more compelling explanation. It assumes that the tiered steps of the pyramid act as a diffraction grating, selectively scattering the sound waves generated by the clap. This selective scattering, based on the wavelength of the sound, leads to a specific pattern of echoes arriving at the listener’s ears at slightly different intervals. The human brain perceives these rapid, periodic variations in arrival time as a change in pitch, creating the characteristic chirping effect. Examining and comparing these models by meticulous simulations result in a more comprehensive understanding of the acoustic marvels embedded within the architecture of Chichen Itza. This research not only contributes to the field of acoustic engineering but also offers valuable insights into the potential role the acoustic considerations may have played in the design and construction of this ancient Mayan monument [4, 5, 6, 7, 8, 9, 10]. 16 IPT Conference Proceedings 14 Decoding Shadows Vinícius dos Passos de Souza, Brazil Understanding a 3D object’s geometry solely by observing its shadow pattern presents a challenging problem in computer vision and optical imaging. In this study, we investigate the feasibility of defining object geometry using Fourier optics principles. Through experiments and computational simulations, we demonstrate that Fourier optics provides a powerful framework for extracting geometric information from shadow patterns. Specifically, we present results showing the successful determination of the length of a cylinder and the radius of a sphere based on their respective shadow patterns. 17 IPT Conference Proceedings 15 Poisson spot Wiktor Kalinowski, Michał Puza Poland Poisson spot is a phenomenon known for 200 years that was crucial in understanding and proving wave properties of light. We approached this well known physics with modern optical techniques and investigated if we can retrieve some geometrical information from diffraction pattern in the shadow. We used Gerchberg-Saxon phase retrieval algorithm to determine the shape of the object casting shadow and succeeded in using it in experiment. 18 IPT Conference Proceedings 16 A geometric approach to diffraction Filippos Typas, Greece A spherical object illuminated by coherent light produces a bright spot in the center of its shadow, known as the Arago-Poisson-Fresnel spot. By shining monochromatic light on solids of various shapes, unique patterns emerge in the shadow region. The purpose of this presentation is to examine the geometric connection of those patterns with the obstacles from which they where formed. Theory extends from the usage of the Fresnel approximation integral to the line integral method and the evolute approach to diffraction. Solids of small dimensions are compared to their corresponding 2D plane projection blocks and were found to provide very similar results in the shadow region, when normal incidence in the Fresnel region is taken into account. Specifically, a metallic tilted cylinder was contrasted to a metallic sheet of the same dimensions, with both resulting in the same diffraction pattern. Intensity graphs of a sphere, a disk and a cylinder of the same cross section were obtained and presented the same diffraction characteristics. Evolute theory is employed on ellipses of increased eccentricity resulting in predominant, bright stretched asteroids with a complex inner structure. Semi-cubical parabolas formed by parabolas, Inverse cardioids from cardioid blocks, evolutes corresponding to a variety of other obstacles are depicted with great accuracy. All in all, we successfully merged different theoretical approaches to observations and matched 3D objects to their 2D projections. 19 IPT Conference Proceedings 17 The Bright Spot Oscar Ernesto Angulo Flores, Mexico The essential framework for understanding the diffraction phenomenon is presented, which is used to explain the peculiar diffraction patterns that appear in the shadows of different objects. A simulation is used to see these results. 20 IPT Conference Proceedings 24 Egg Fight Matvei Anoshin, Team IPT To predict the winner of a given egg fight, a non-invasive evaluation pipeline has been developed that includes size measurement, acoustic determination of the eggshell’s eigenfrequency, and ovoscopy for precise analysis of the eggshell surface. After the pipeline is completed, the egg is boiled and then knocked against another one. Then, the radius of curvature at the contact point is derived from the contact angle and an approximated egg shape. These data, along with COMSOL simulations, allow to estimate the egg’s Young’s modulus from its eigenfrequency, thereby providing all required information to describe an egg fight as a process of stress distribution between shells until one breaks due to reaching the maximum pressure caused by the buckling effect. Final prediction was performed using both supervised and unsupervised approaches. In the unsupervised approach, the eggshell strength function σcrit(E,r, ...)was expanded into a Taylor series and then optimized as a multivariate function. For the supervised approach, the Gaussian Naive Bayes algorithm was used due to the independence of the measured properties and their approximately normal distribution. These techniques resulted in a non-invasive winner prediction accuracy of 88.8%. After including the invasively measured eggshell thickness, the prediction accuracy increased to 91%. 27 IPT Conference Proceedings Bibliography [1] Tadashi F Tokieda. “The hopping hoop”. In: The American mathematical monthly 104.2 (1997), pp. 152–154. [2] Timothy Pritchett. “The hopping hoop revisited”. In: The American mathematical monthly 106.7 (1999), pp. 609–617. [3] WFD Theron and Milton F Maritz. “The amazing variety of motions of a loaded hoop”. In: Mathematical and computer modelling 47.9-10 (2008), pp. 1077–1088. 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