📘 These experiments are part of our complete guide Doing Physics with a Smartphone: The Complete Guide, from middle school to university.
Did you know that with a simple smartphone, you can reproduce experiments designed by some of history’s greatest scientists? In this article, we invite you to conduct 12 experiments conceived by renowned figures such as Pythagoras, Robert Boyle, and Albert Einstein. These experiments, accessible to everyone, require no complex apparatus. Are you ready to discover the work of our predecessors and immerse yourself in fascinating scientific discoveries? Get your smartphones ready!
Table of Contents
Pythagoras and the Musical Scale - Galileo and the Pendulum - Torricelli and Water Flow - Newton and Gravitation - Leibniz and Energy Conservation - Boyle and Sound Waves - Einstein and the Elevator Thought Experiment - Doppler and the Doppler Effect - Nollet and Measuring the Speed of Sound - Young and Color Theory - Delambre and Measuring the Meridian - Von Helmholtz and the Resonator
Pythagoras and the Musical Scale
Legend has it that one day, while walking near a forge, Pythagoras was struck by the harmonious sounds produced by hammers striking an anvil. Intrigued, he noticed that the pitch of the sounds depended on the size and weight of the hammers. He then conducted experiments by suspending different weights from strings and striking them, discovering that specific weight ratios produced harmonious sounds. Pythagoras identified three fundamental musical intervals: the octave (ratio 1:2), the fifth (ratio 2:3), and the fourth (ratio 3:4). These intervals formed the basis of the Pythagorean diatonic scale.
Pythagoras, one of the greatest geniuses of ancient Greece (570-495 BCE), was a mathematician, philosopher, musician, and mystic. As founder of the Pythagorean movement, he emphasized mathematics, music, and universal harmony. His contributions include the famous Pythagorean theorem, and his interest in music led him to explore musical intervals and the concept of the “harmony of the spheres.”
To perform an analysis similar to Pythagoras’s and rediscover his insights, we suggest using the FizziQ app’s sound synthesizer to experimentally determine which frequency combinations sound harmonious. Try, for example, choosing a base frequency of 600 hertz, then adding a second channel, and identify the “harmonic” chords. Are they the same as those found by Pythagoras? Do Pythagorean intervals sound different from other chords? Analyze these chords with the app’s oscilloscope to understand why they are pleasant to the ear. To learn more about sound waves and harmonic chords, see our article: Can You See Sound? You can also try the activity Tubular Melodies to explore musical intervals.
Galileo and the Pendulum
Everyone knows the anecdote of Galileo dropping weights from the top of the Leaning Tower of Pisa, the tilted structure that forms part of Pisa Cathedral’s architectural ensemble, a masterpiece of Romanesque architecture built between the 11th and 12th centuries. A less well-known story takes place inside this cathedral. While a medical student at the university, Galileo noticed a suspended lamp swinging during a religious service. Intrigued by the lamp’s regular motion, he used his pulse to time the oscillations and found that, regardless of the swing’s amplitude, the period of oscillations remained remarkably constant. This observation marked the beginning of his experiments with pendulums, contributing significantly to classical physics, particularly to precise time measurement and the development of mechanical theory.
A hundred years later, Christiaan Huygens confirmed Galileo’s hypothesis and provided a model for the simple pendulum whose oscillation period depends only on the length of the string and gravity. For small oscillations: T = 2π × √(l/g), where T is the period in seconds, l is the string length in meters, and g is the acceleration due to gravity in meters per second squared.
You can experimentally demonstrate this relationship with a smartphone. Attach a hook to the ceiling and tie a long rope with a smartphone at the end, secured in a plastic pouch, then set it swinging. The period can be measured in multiple ways using smartphone sensors, for example by measuring acceleration, magnetic field variations relative to a magnet on the floor, or brightness by placing the smartphone on the floor with a ball at the pendulum’s end that blocks the detector. If you have a Newton’s cradle, verify the regularity of oscillations by measuring the time between impacts using sound level measurement.
To learn more, discover our activities on pendulums: Simple Pendulum, Period of a Pendulum, and Newton’s Pendulum.
Torricelli and Water Flow
Evangelista Torricelli (1608-1647) was an Italian mathematician and physicist, primarily known for inventing the mercury barometer. A student of Galileo Galilei, Torricelli continued his work on atmospheric pressure and fluids, developing fundamental principles of fluid dynamics. At the time, scientists didn’t understand why water pumps couldn’t lift water beyond 10 meters. Torricelli hypothesized that air pressure exerted on the water in the basin balanced the water column. To test this idea, he filled a tube with mercury, denser than water, and inverted it in a basin of mercury. A 76 cm column of mercury remained, creating a vacuum in the upper part, equivalent to a 10 m water column accounting for mercury’s density (13.6). This experiment proved the existence of atmospheric pressure and vacuum, laying the foundations for modern meteorology and fluid physics.
Another contribution from the scientist is Torricelli’s law, which explains that the flow velocity of a fluid through an orifice below a reservoir is proportional to the square root of the fluid height above the orifice. Formally, the velocity v is given by v = √(2gh), where g is gravitational acceleration and h is the height of the fluid column. This law derives from energy conservation principles and fluid dynamics, illustrating how pressure and height influence flow rate.
To reproduce this experiment, you can perform the following simple experiment: choose a water bottle and pierce a hole near its bottom. Then film the bottle with a smartphone as it empties. This video can be analyzed using kinematic analysis to observe the relationship between water height and flow velocity.
Newton and Gravitation
Isaac Newton’s discovery of gravitation is one of the most famous legends in the history of science, often embellished by the anecdote of the apple falling from a tree. While this story is popular, the true way Newton formulated his theory of universal gravitation is more complex and rests on years of research and meticulous observations. By the mid-1660s, Newton was already deeply engaged in studying physics and mathematics at Cambridge University. When a plague epidemic forced the university to close in 1665, Newton returned to Woolsthorpe, his hometown. It was during this period of forced retreat, known as his “annus mirabilis” or miraculous year, that he began developing his revolutionary ideas in physics.
The famous apple story suggests that Newton was inspired to formulate his theory of gravitation after seeing an apple fall from a tree. According to accounts reported by William Stukeley, a friend of Newton, and John Conduitt, his son-in-law, Newton told them that the apple incident made him reflect on the nature of the force that made the apple fall perpendicular to the ground. However, Newton’s true breakthrough was not simply realizing that objects fall toward Earth, but rather generalizing this attraction to understand that all bodies in the universe attract each other mutually. Newton began thinking that the same force that made the apple fall was also responsible for keeping planets in orbit around the Sun. He formulated his law of universal gravitation, which states that every particle of matter in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This work was published in 1687 in his major work, “Philosophiae Naturalis Principia Mathematica” (Mathematical Principles of Natural Philosophy), which established the foundations of classical mechanics.
To better understand gravity, you can drop your smartphone instead of an apple. Such an experiment will quickly provide an estimate of g by measuring the fall duration from a certain height. Of course, you must ensure the smartphone lands on a soft surface and precisely measure both the height and the elapsed time during the fall. Follow the activity protocol Galileo or explore variations in g with Latitude and Gravity.
Leibniz and Energy Conservation
Gottfried Wilhelm Leibniz (1646-1716) was a German polymath, recognized for his significant contributions to philosophy, mathematics, logic, theology, and science. Born in Leipzig to a family of jurists, Leibniz showed remarkable intelligence and insatiable curiosity for various fields of knowledge from a young age. A polyglot, he mastered several languages including Latin, Greek, French, and German, and had some knowledge of English, Italian, and Dutch. This interest in languages led him to propose ideas for improving human communication efficiency, particularly by working on developing a universal language, or “characteristica universalis,” based on a logical system of symbols to represent concepts. He believed this universal language could not only facilitate communication between different peoples but also help resolve philosophical or scientific disputes by clarifying concepts. Despite his efforts and extensive research, he never succeeded in implementing this idea.
Leibniz was not convinced by the Cartesian view that the quantity of motion (the product of mass and velocity) was conserved in collisions. He observed that this theory did not account for all experimental observations, particularly those of elastic collisions, where the sum of the products of mass and velocity seemed to vary. To resolve this inconsistency, Leibniz proposed the concept of “vis viva” (living force), which he defined as the product of mass and the square of velocity (mv²). He demonstrated that in an isolated system, the sum of these vis viva was conserved, even if the quantity of motion was not necessarily conserved. This innovative idea laid the foundations for our modern understanding of kinetic energy, highlighting the importance of energy conservation in mechanical phenomena.
Many experiments can be conducted with a smartphone to illustrate energy conservation during collisions. For the best study, use the FizziQ app’s kinematic module. With a smartphone, film an elastic collision then an inelastic collision, and study the conservation laws of momentum and energy. Try the activity Billiards to study collisions and energy conservation, or use the activity Newton’s Pendulum to observe energy transfers.
Boyle and Sound Waves
Robert Boyle (1627-1691), an Irish chemist and physicist, is considered one of the founders of modern chemistry. He is best known for Boyle’s law, which describes the inverse relationship between the pressure and volume of a gas at constant temperature. His experiments with a vacuum pump demonstrated the importance of atmospheric pressure and laid the foundations for physical chemistry. One of his most famous experiments involved a tortoise placed in a vacuum chamber to observe the effects of vacuum on a living organism. Boyle and his assistant, Robert Hooke, noted that as they removed air from the chamber, the tortoise became increasingly inactive. They quickly reintroduced air before the tortoise suffered permanent damage, thus dramatically demonstrating the importance of air for the survival of living beings.
From this observation, Boyle conducted numerous experiments, particularly on sound propagation. He showed that sound cannot propagate in a vacuum by placing a chiming clock in a glass bell connected to a vacuum pump. By gradually removing air from the bell, he observed that the clock’s sound became fainter and fainter until it became inaudible when the vacuum was nearly complete. This experiment proved that sound requires a material medium, like air, to propagate, confirming that vacuum is an effective acoustic insulator and illustrating the principles of sound wave transmission.
You can reproduce such an experiment using a jar in which you can reduce atmospheric pressure, like those used for food preservation, or better still, a laboratory vacuum bell. Place a smartphone emitting a constant-intensity sound inside the jar, with the smartphone also measuring atmospheric pressure (Apple smartphones include atmospheric pressure sensors). Outside the bell, measure sound intensity with another smartphone. By gradually reducing pressure in the bell, measure the decrease in sound intensity. You will verify that sound intensity decreases logarithmically as the pressure in the bell decreases.
Einstein and the Elevator Thought Experiment
A thought experiment is a hypothetical scenario used to explore the consequences of a principle or theory in the absence of actual physical experimentation. It consists of reasoning about a problem using only imagination and knowledge of physical laws, without requiring empirical evidence or practical execution. Used in various fields, including physics, philosophy, mathematics, and ethics, thought experiments serve as powerful tools for conceptualizing ideas, challenging existing notions, and stimulating intellectual exploration. Albert Einstein, one of the most eminent users of thought experiments, widely employed them to develop his revolutionary theories in physics, particularly the theories of special and general relativity. These experiments allowed him to visualize complex problems and paradoxes in physics that were difficult or impossible to test with the technology of his time.
One of Einstein’s most famous thought experiments concerns the theory of general relativity: the elevator experiment. Einstein imagined himself inside a closed elevator in deep space, accelerating upward. A ball dropped inside the elevator appears to fall toward the floor similarly to Earth’s gravitational attraction. In contrast, a stationary elevator near a planet experiences a similar effect due to gravity. The essence of this experiment is that, within the confines of the elevator, one cannot distinguish between the effects of gravity and pure acceleration.
To conduct this experiment, place a smartphone on a table and open the Absolute Acceleration measurement instrument in the FizziQ app. You will see the value of 9.80 m/s², corresponding to gravitational acceleration. Then place a mattress on the floor, or use a soft bed, press the record button, then toss the smartphone so it describes a parabola and falls onto the mattress. After stopping the recording and adding the data to the experiment notebook, you will notice that during the entire time in the air, the measured acceleration is zero. Although the smartphone is in free fall, and therefore its vertical velocity varies for an observer on Earth, the smartphone itself perceives no force—it is weightless.
This experiment exactly reproduces Einstein’s elevator thought experiment. The smartphone is equivalent to an elevator falling with the same acceleration as gravity. Inside the smartphone, the accelerometer cannot detect whether it is in free fall or whether gravity is zero. For it, as for a person in the elevator, gravity is equivalent to acceleration.
To learn more, try the activity Einstein’s Elevator or Galileo.
Doppler and the Doppler Effect
In 1842, Christian Doppler, an Austrian physicist, proposed a new theory about the frequency shift of a wave when the source moves relative to the observer. His theory was met with great skepticism by the scientific community, mainly because the means of transportation at the time did not allow clear demonstration of what the theory predicted. However, irrefutable proof of Doppler’s theory was provided in 1845 by meteorologist Buys-Ballot. He organized a spectacular experiment by placing musicians on a train platform traveling at 70 km/h, having them play a constant note. People along the route could observe the frequency change of the sounds emitted by the orchestra as the train passed them, confirming that the Doppler effect was not an illusion.
The frequency of a wave, whether sound or light, is affected by the motion of the source relative to the observer. This frequency shift is directly proportional to velocity, according to the equation: Δf = f × V_mobile / V_wave, where V_mobile is the velocity of the moving object and V_wave is the wave velocity.
Today, the Doppler effect is used in many technologies, such as weather radar, medical imaging, and speed monitoring. It has proven to be a valuable tool for astronomers, allowing them to understand celestial movements and discover new objects like exoplanets. From humble beginnings in Doppler’s laboratory to modern observatories scanning the depths of space, the Doppler effect has shaped our understanding of the universe, offering windows into the motion and composition of celestial bodies.
Many experiments can be conducted with a smartphone to demonstrate and experimentally verify Doppler’s law. For this, you can use the smartphones’ sound synthesizer to generate sounds and measure sound frequency using the microphone. These experiments allow you to concretely demonstrate the frequency shift observed when the sound source is moving relative to the observer. Try the activity Doppler Effect or discover the activity Sound Pendulum to simulate exoplanet detection.
Nollet and Measuring the Speed of Sound
Jean-Antoine Nollet (1700-1770), also known as Abbé Nollet, was a French physicist and priest renowned for his contributions to the study of electricity and acoustics. Born in Pimprez, Nollet began his career in theology before turning to the natural sciences. He became a member of the Academy of Sciences and taught experimental physics at the Collège de Navarre in Paris. Nollet is best known for his work on electricity. He was one of the first to demonstrate the effects of static electricity and to popularize electrical experiments in Europe. He invented the electrometer, a device for measuring electric charge, and performed spectacular public demonstrations that captured the imagination of his era.
In 1738, the Academy of Sciences tasked Nollet with precisely determining the speed of sound. Using the topography of the Paris basin, Nollet placed a cannon on the tower of Montlhéry, with observers posted on the Montmartre hill, 28 kilometers away. At night, they timed the interval between seeing the flash of light and hearing the “BANG” of a cannon shot. Since the light from the shot was perceived almost instantaneously, they then measured the time needed to hear the sound. Nollet calculated the speed of sound using the measured distance and time, reporting a speed of 337.2 meters per second to the Academy of Sciences. This value, very close to the modern measurement (about 343 m/s at 20°C), demonstrated the precision and rigor of his scientific method. His experiment marked a turning point in the study of sound waves and remains a striking example of the practical application of scientific principles.
You can easily reproduce this experiment in class or at home with two smartphones equipped with the FizziQ app. To do this, use the app’s acoustic chronometers, which measure the time elapsed between two sound events. Place the two smartphones side by side and trigger the chronometers by clapping your hands. Then move one of the phones at least 5 meters away and clap your hands again near the other phone. The chronometers stop and the speed of sound can be calculated by dividing the distance by the time difference between the two chronometers. To perform this experiment, follow the activity Speed of Sound.
Young and Color Theory
Thomas Young, a British physicist and polymath, is famous for his revolutionary work on color theory and trichromatic vision. At the beginning of the 19th century, Young became interested in how the human eye perceives colors. In 1801, he proposed that color vision relies on three types of receptors in the eye, each sensitive to one of three primary colors: red, green, and blue. To test his theory, Young used colored filters and light sources of different wavelengths. He demonstrated that combining these three basic colors could reproduce all other colors perceivable by the human eye. For example, by combining red and green lights, he could create yellow; by combining blue and red, he obtained magenta; and by combining all three, he obtained white.
It took more than 150 years before the existence of cells sensitive to three different wavelength ranges (most sensitive to green-yellow, green-blue, and blue—not red, green, and blue) was confirmed. These cells were identified in 1956 by Gunnar Svaetichin. In 1983, this discovery was validated in human retinas during an experiment conducted by Herbert Dartnall, James Bowmaker, and John Mollon, who obtained microspectrophotometric readings of individual cones in human eyes. This discovery has had a profound influence on the science of optics, the understanding of visual perception, and has also been fundamental to the development of modern technologies such as television and computer screens, which use red, green, and blue pixels to display a full range of colors.
To experimentally reproduce Thomas Young’s experiment with a smartphone, follow this experiment: using the Color instrument in the FizziQ app, point at a color and add this measurement to the experiment notebook. This measurement will give you the amounts of primary colors red, green, and blue that make up this color. Using the Color Synthesizer in Tools with the amounts determined by the spectrum, you can then reconstruct this color. Whatever the color, it can be recomposed from the three main colors. The three primary colors, mixed together, are therefore sufficient to create any color we perceive. Explore this principle with the activity RGB Additive Synthesis or Fall Colors.
Delambre and Measuring the Meridian
In 1790, the French National Assembly decided to establish a unified measurement system, using the Earth as a reference. The meter was then defined as one ten-millionth of the quarter of the Earth’s meridian. Pierre Méchain and Jean-Baptiste Delambre, astronomers and mathematicians, were tasked with measuring this meridian in 1792 to establish the most precise estimate possible of the distance between Dunkirk and Barcelona.
What followed for the two scientists was a seven-year adventure. The period of Revolutionary Terror made travel perilous, especially with an unusual measuring device, the repeating circle. Delambre often had to face suspicious and uncooperative National Guards, which prevented him from working for an entire year. Méchain, initially luckier, saw his efforts complicated in 1793 when Spain declared war on France. This tense political situation hindered his work and movements. Moreover, Méchain discovered an anomaly of a few arc seconds in his measurements, which led him to hide his results for fear of discredit. These logistical, political, and personal challenges seriously complicated the mission to define the meter as one ten-millionth of the quarter of the Earth’s meridian. In 1799, they finally determined the meter’s length at 0.513074 toises. Méchain, facing an anomaly in his measurements, chose to conceal them. Their work laid the foundations for the modern meter’s definition.
Triangulation is the basic mathematical tool used by both scientists. It is a geometric method used to determine the precise position of a point by measuring angles from two fixed and known reference points. This procedure relies on creating triangles for which distances between points can be calculated using trigonometry laws. In practice, one begins by measuring a baseline between two fixed points, then measures the angles between this baseline and a visible third point. From these measurements, the distance to the third point can be calculated. By repeating this process, a series of triangles is formed, allowing large areas to be mapped with great precision.
A triangulation exercise can be performed simply using the FizziQ app’s theodolite. This exercise allows, for example, calculating distances that are too great or where obstacles exist, making direct measurement impossible. Try the activity Triangulation to measure inaccessible distances.
Von Helmholtz and the Resonator
Hermann von Helmholtz was a German scientist famous for his contributions to many fields, including physics, physiology, and psychology. A particularly interesting anecdote about Helmholtz relates to his invention of the Helmholtz resonator, developed to identify the different frequencies of sounds produced by various musical instruments.
In his quest to understand how humans perceive sounds, Helmholtz designed a series of spheres of different sizes with narrow openings. These spheres, called Helmholtz resonators, were intended to vibrate in resonance with specific frequencies. Helmholtz used these resonators by placing them near his ear to listen to sounds produced by different instruments. Each resonator was calibrated to amplify a particular frequency, allowing Helmholtz to very precisely analyze the sound spectrum of music.
You can easily build a Helmholtz resonator using a test tube. By blowing across the tube, a sound is emitted whose frequency is specific to the tube’s geometry. For a closed tube, the fundamental resonance frequency is: f₀ = c / (4L + 1.6D), where L is the tube length and D is the tube diameter. Using the FizziQ app’s frequency meter, you can verify that the frequency of the emitted sound matches the calculated resonance frequency of the tube.
Another fun experiment is to measure the frequency of the “pop” emitted when opening a wine bottle. This frequency depends on the cavity between the liquid and the cork. The theoretical frequency of the sound can also be calculated and verified with the appropriate tools. Try the activity Helmholtz to explore acoustic resonators.
Conclusion
Exploring scientists and the experiments they conducted brings science and its progress to life. Thanks to smartphones and tablets, students can quickly perform experiments that allow them to step into the shoes of great scientists and understand the problems they tried to solve. These activities not only enrich students’ scientific understanding but also make learning interactive and engaging. To learn more about using smartphones or tablets in science classes, you can read our article on the subject: Using FizziQ in the Classroom.